OEIS/A220952 - Revision history

imported>Gfis: /* Why is it so fascinating? */ typos

2019-04-14T03:25:00Z

Why is it so fascinating?: typos

← Older revision		Revision as of 03:25, 14 April 2019
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	===Why is it so fascinating?===		===Why is it so fascinating?===
	Maybe (also?) because it is a [https://en.wikipedia.org/wiki/FASS_curve FASS curve]]. '''[[OEIS/FASS curves\|Please read on]]''' what have ~~looked~~ for in the meantime.		Maybe (also?) because it is a [https://en.wikipedia.org/wiki/FASS_curve FASS curve]. '''[[OEIS/FASS curves\|Please read on]]''' to see what I have collected for these curves in the meantime.

imported>Gfis: fascinating

2017-10-17T19:15:53Z

fascinating

@@ Line 1: / Line 1: @@
-Don Knuth found this [https://oeis.org/search?q=A220952 sequence] "so fascinating":
+Don Knuth found this [https://oeis.org/search?q=A220952 sequence] so fascinating:
 , 1, 2, 3, 4, 9, 14, 19, 18, 17, 16, 11, 12, 13, 8, 7, 6, 5, 10, 15, 20, 21, 22, 23, 24, 49
 I stumbled over it when looking for OEIS sequences with keyword <code>unkn</code>.
 ===Observations===
-Here are the values listed in base 10 and base 5:
+The values listed in base 5 are: 00,01,02,03,04,14,24,34,33,32,31,21,22,23,13,12,11,10,20,30,40,41,42,43,44,144
 Some elementary observations and conditions (disregarding the trailing 49):
-* A permutation of the numbers 0..24
+* a(n=0..24) is a permutation of the numbers 0..24
 * a(n=0..12) = 24 - a(24-n)
 * Symmetricy around n=12, a(12) = 2*(5<sup>1</sup> + 5<sup>0</sup>)
@@ Line 66: / Line 38: @@
 ===Why is it so fascinating?===
-Maybe (also?) because it is a [https://en.wikipedia.org/wiki/FASS_curve FASS curve]]. '''[[OEIS/FASS curves|Please read on]]''' why I am fascinated in the meantime.
+Maybe (also?) because it is a [https://en.wikipedia.org/wiki/FASS_curve FASS curve]]. '''[[OEIS/FASS curves|Please read on]]''' what have looked for in the meantime.

imported>Gfis: gen_meander.pl and FASS

2017-09-10T17:24:16Z

gen_meander.pl and FASS

← Older revision		Revision as of 17:24, 10 September 2017
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	109,114,119,118,117,116,111,112,113,108,107,106,105,110,115,120,121,122,123,124,		109,114,119,118,117,116,111,112,113,108,107,106,105,110,115,120,121,122,123,124,
	249		249
	I would have explained this proposal (for generation 3) as follows: For the "Z"s on the main diagonal, the upper, horizontal stroke consists of 4 nodes spanning a lenthagth of 3*5<sup>n</sup>. Before that upper stroke and behind the lower stroke there is a "handle" consisting of the shape of generation 2. Whenever the generation 2 shape occurs again in the ~~squence~~, it is mirrored on the vertical axis. Please note that the "shape" of generation 1 consists of the values 1,2,3 which are also visible - each time mirrored - on the "/"-stroke of generation 2.		I would have explained this proposal (for generation 3) as follows: For the "Z"s on the main diagonal, the upper, horizontal stroke consists of 4 nodes spanning a lenthagth of 3*5<sup>n</sup>. Before that upper stroke and behind the lower stroke there is a "handle" consisting of the shape of generation 2. Whenever the generation 2 shape occurs again in the sequence, it is mirrored on the vertical axis. Please note that the "shape" of generation 1 consists of the values 1,2,3 which are also visible - each time mirrored - on the "/"-stroke of generation 2.

	~~===History of Sequence A220952===~~
	Since sequence [https://oeis.org/search?q=A220952 A220952] still had the status '''unkn''' after 4 years, I wrote my proposal to the [http://list.seqfan.eu/ Seqfan Mailing list]. The discussion there showed quickly that this solution was not the desired one. There proposed my the I wrote
	~~===Explanation of Generation 3===~~
	~~Therefore I hope to be able to write a generating program for higher powers of 5. But I have no idea for additional properties of this sequence.~~

	~~===Variants===~~
	For generation 2, the program which evaluates the conditions above found 2 similiar variants:		For generation 2, the program which evaluates the conditions above found 2 similiar variants:
	* 0, 1,2,3,4, 9,8,13,14,19,18,17,12,7,6,5,10,11,16,15,20,21,22,23,24 - [http://www.teherba.org/images/6/64/Z53.var_a.svg a "Z" shape with broken horizontal strokes]		* 0, 1,2,3,4, 9,8,13,14,19,18,17,12,7,6,5,10,11,16,15,20,21,22,23,24 - [http://www.teherba.org/images/6/64/Z53.var_a.svg a "Z" shape with broken horizontal strokes]
	* 0, 1,2,3,4, 9,8,7,6,5,10,11,12,13,14,19,18,17,16,15,20,21,22,23,24 - [http://www.teherba.org/images/8/89/Z53.var_b.svg 2 small "Z" shapes]		* 0, 1,2,3,4, 9,8,7,6,5,10,11,12,13,14,19,18,17,16,15,20,21,22,23,24 - [http://www.teherba.org/images/8/89/Z53.var_b.svg 2 small "Z" shapes]
	~~I suppose that these patterns may be expanded in the same way as A220952.~~

	[~~mailto~~: ~~georg dot fischer at t hyphen online dot de~~ - ~~Georg Fischer] 2017~~-08-25		===History of Sequence A220952===
			Since sequence [https://oeis.org/search?q=A220952 A220952] still had the keyword '''unkn''' after 4 years, I wrote my proposal to the [http://list.seqfan.eu/ Seqfan Mailing list]. The discussion there showed quickly that:
			* The problem had been stated by Donald Knuth in more detail in ''A twisted enumeration of the positive integers''; Problem 11733, Amer. Math. Monthly, 120 (9) (2013), 76.
			* It was solved by Richard Stong in [https://lupucezar.files.wordpress.com/2011/02/amer-math-monthly-123-1-97.pdf Amer. Math. Monthly, 123 (1) (2016), 98-100].
			The entry for the sequence was written by R. J. Mathar, together with a Maple program. Since I do not have a Maple license, I wrote [[OEIS/gen_meander.pl\|Perl program]] which generates the same output.

			===Why is it so fascinating?===
			Maybe (also?) because it is a [https://en.wikipedia.org/wiki/FASS_curve FASS curve]]. '''[[OEIS/FASS curves\|Please read on]]''' why I am fascinated in the meantime.

imported>Gfis at 16:45, 10 September 2017

2017-09-10T16:45:48Z

← Older revision		Revision as of 16:45, 10 September 2017
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	I stumbled over it when looking for OEIS sequences with keyword <code>unkn</code>.		I stumbled over it when looking for OEIS sequences with keyword <code>unkn</code>.
	===Observations===		===Observations===
	Here are the values listed in base 5:		Here are the values listed in base 10 and base 5:
	n a(n) base 5		n a(n) base 5
	===================		===================
	0 0 0		0 0 0
	~~-------------------~~
	1 1 1		1 1 1
	2 2 2		2 2 2
	3 3 3		3 3 3
	4 4 4		4 4 4
	~~-------------------~~
	5 9 14		5 9 14
	6 14 24		6 14 24
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	23 23 43		23 23 43
	24 24 44		24 24 44
	~~-------------------~~
	25 49 144		25 49 144

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	In the following I will refer to ''generations'' which correspond to the powers of 5. Knuth's values are generations 0,1,2 and the first of 3 (49).		In the following I will refer to ''generations'' which correspond to the powers of 5. Knuth's values are generations 0,1,2 and the first of 3 (49).

	I wrote a Perl program which plots the values of b-files with SVG. The [http://www.teherba.org/images/0/03/A220952.orig.svg image] shows a slighty distorted "Z" shape with "handles" on the diagonal. The nodes' values are showed in base 5. With another Perl program I tried to generate the starting 26 values, and a continuation up to the next power of 5 (125). The program did maintain the conditions noted above, but returned ten thousands of "unpleasant solutions". The conditions seem not to be strong enough.		I wrote a Perl program which plots the values of b-files with SVG. The [http://www.teherba.org/images/0/03/A220952.orig.svg image] shows a slighty distorted "Z" shape with "handles" on the diagonal. The nodes' values are showed in base 5.
	===Proposal===		===First Proposal===
	Then I produced a big sheet of quad paper and tried to extend the basic shape to 125 elements. Please have a look at '''[http://www.teherba.org/images/7/71/Z53.svg my proposal]''' for a continuation with some "fractal" appearance.		Then I produced a big sheet of quad paper and tried to extend the basic shape to 125 elements. Please have a look at '''[http://www.teherba.org/images/7/71/Z53.svg my proposal]''' for a continuation with some "fractal" appearance.

	I ~~think~~ that a(n=0..125) could read:		I thought that a(n=0..125) could read:
	1, 2,3,4,9, 14,19,18,17,16,11,12,13,8,7,6,5,10,15,20,21,22,23,24,		1, 2,3,4,9, 14,19,18,17,16,11,12,13,8,7,6,5,10,15,20,21,22,23,24,
	49,74,99,98,97,96,95,90,85,80,81,82,83,88,87,86,91,92,93,94,89,84,79,78,77,76,51,		49,74,99,98,97,96,95,90,85,80,81,82,83,88,87,86,91,92,93,94,89,84,79,78,77,76,51,
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	109,114,119,118,117,116,111,112,113,108,107,106,105,110,115,120,121,122,123,124,		109,114,119,118,117,116,111,112,113,108,107,106,105,110,115,120,121,122,123,124,
	249		249
			I would have explained this proposal (for generation 3) as follows: For the "Z"s on the main diagonal, the upper, horizontal stroke consists of 4 nodes spanning a lenthagth of 3*5<sup>n</sup>. Before that upper stroke and behind the lower stroke there is a "handle" consisting of the shape of generation 2. Whenever the generation 2 shape occurs again in the squence, it is mirrored on the vertical axis. Please note that the "shape" of generation 1 consists of the values 1,2,3 which are also visible - each time mirrored - on the "/"-stroke of generation 2.

			===History of Sequence A220952===
			Since sequence [https://oeis.org/search?q=A220952 A220952] still had the status '''unkn''' after 4 years, I wrote my proposal to the [http://list.seqfan.eu/ Seqfan Mailing list]. The discussion there showed quickly that this solution was not the desired one. There proposed my the I wrote
	===Explanation of Generation 3===		===Explanation of Generation 3===
	For the "Z"s on the main diagonal, the upper, horizontal stroke consists of 4 nodes spanning a length of 3*5<sup>n</sup>. Before that upper stroke and behind the lower stroke there is a "handle" consisting of the shape of generation 2. Whenever the generation 2 shape occurs again in the squence, it is mirrored on the vertical axis. Please note that the "shape" of generation 1 consists of the values 1,2,3 which are also visible - each time mirrored - on the "/"-stroke of generation 2.

	Therefore I hope to be able to write a generating program for higher powers of 5. But I have no idea for additional properties of this sequence.		Therefore I hope to be able to write a generating program for higher powers of 5. But I have no idea for additional properties of this sequence.

imported>Gfis: typo

2017-08-25T11:06:00Z

typo

← Older revision		Revision as of 11:06, 25 August 2017
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	* Only one base-5 digit is incremented or decremented by 1 (without carry) in each step.		* Only one base-5 digit is incremented or decremented by 1 (without carry) in each step.

	In the following I will refer to ''generations'' which correspond to the powers of 5. Knuth's values are ~~generation~~ 2 and the first of ~~geneartion3~~ (49).		In the following I will refer to ''generations'' which correspond to the powers of 5. Knuth's values are generations 0,1,2 and the first of 3 (49).

	I wrote a Perl program which plots the values of b-files with SVG. The [http://www.teherba.org/images/0/03/A220952.orig.svg image] shows a slighty distorted "Z" shape with "handles" on the diagonal. The nodes' values are showed in base 5. With another Perl program I tried to generate the starting 26 values, and a continuation up to the next power of 5 (125). The program did maintain the conditions noted above, but returned ten thousands of "unpleasant solutions". The conditions seem not to be strong enough.		I wrote a Perl program which plots the values of b-files with SVG. The [http://www.teherba.org/images/0/03/A220952.orig.svg image] shows a slighty distorted "Z" shape with "handles" on the diagonal. The nodes' values are showed in base 5. With another Perl program I tried to generate the starting 26 values, and a continuation up to the next power of 5 (125). The program did maintain the conditions noted above, but returned ten thousands of "unpleasant solutions". The conditions seem not to be strong enough.

imported>Gfis: Variants

2017-08-25T11:04:12Z

Variants

← Older revision		Revision as of 11:04, 25 August 2017
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	Therefore I hope to be able to write a generating program for higher powers of 5. But I have no idea for additional properties of this sequence.		Therefore I hope to be able to write a generating program for higher powers of 5. But I have no idea for additional properties of this sequence.

			===Variants===
			For generation 2, the program which evaluates the conditions above found 2 similiar variants:
			* 0, 1,2,3,4, 9,8,13,14,19,18,17,12,7,6,5,10,11,16,15,20,21,22,23,24 - [http://www.teherba.org/images/6/64/Z53.var_a.svg a "Z" shape with broken horizontal strokes]
			* 0, 1,2,3,4, 9,8,7,6,5,10,11,12,13,14,19,18,17,16,15,20,21,22,23,24 - [http://www.teherba.org/images/8/89/Z53.var_b.svg 2 small "Z" shapes]
			I suppose that these patterns may be expanded in the same way as A220952.

			[mailto: georg dot fischer at t hyphen online dot de - Georg Fischer] 2017-08-25

imported>Gfis: plusmn power of 5 condition

2017-08-25T10:13:21Z

plusmn power of 5 condition

← Older revision		Revision as of 10:13, 25 August 2017
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	25 49 144		25 49 144

	Some elementary conditions (disregarding the trailing 49):		Some elementary observations and conditions (disregarding the trailing 49):
	* A permutation of the numbers 0..24		* A permutation of the numbers 0..24
	* a(n=0..12) = 24 - a(24-n)		* a(n=0..12) = 24 - a(24-n)
	* Symmetricy around n=12, a(12) = 2*(5<sup>1</sup> + 5<sup>0</sup>)		* Symmetricy around n=12, a(12) = 2*(5<sup>1</sup> + 5<sup>0</sup>)
	* Groups of length 5<sup>n</sup> - 1, n=0,1,2 ...		* Groups of length 5<sup>n</sup> - 1, n=0,1,2 ...
			* Only one base-5 digit is incremented or decremented by 1 (without carry) in each step.

	In the following I will refer to ''generations'' which correspond to the powers of 5. Knuth's values are generation 2 and the first of geneartion3 (49).		In the following I will refer to ''generations'' which correspond to the powers of 5. Knuth's values are generation 2 and the first of geneartion3 (49).

imported>Gfis: typo

2017-08-24T21:33:00Z

typo

← Older revision		Revision as of 21:33, 24 August 2017
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	For the "Z"s on the main diagonal, the upper, horizontal stroke consists of 4 nodes spanning a length of 3*5<sup>n</sup>. Before that upper stroke and behind the lower stroke there is a "handle" consisting of the shape of generation 2. Whenever the generation 2 shape occurs again in the squence, it is mirrored on the vertical axis. Please note that the "shape" of generation 1 consists of the values 1,2,3 which are also visible - each time mirrored - on the "/"-stroke of generation 2.		For the "Z"s on the main diagonal, the upper, horizontal stroke consists of 4 nodes spanning a length of 3*5<sup>n</sup>. Before that upper stroke and behind the lower stroke there is a "handle" consisting of the shape of generation 2. Whenever the generation 2 shape occurs again in the squence, it is mirrored on the vertical axis. Please note that the "shape" of generation 1 consists of the values 1,2,3 which are also visible - each time mirrored - on the "/"-stroke of generation 2.

	Therefore I hope to be able to write a generating program for higher powers of 5. ~~Bbut~~ I have no idea for additional properties of this sequence.		Therefore I hope to be able to write a generating program for higher powers of 5. But I have no idea for additional properties of this sequence.

imported>Gfis: proposal

2017-08-24T21:25:34Z

proposal

← Older revision		Revision as of 21:25, 24 August 2017
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	I think that a(n=0..125) could read:		I think that a(n=0..125) could read:
	1,2,3,4,9, 14,19,18,17,16,11,12,13,8,7,6,5,10,15,20,21,22,23,24,		1, 2,3,4,9, 14,19,18,17,16,11,12,13,8,7,6,5,10,15,20,21,22,23,24,
	49,74,99,98,97,96,95,90,85,80,81,82,83,88,87,86,91,92,93,94,89,84,79,78,77,76,51,		49,74,99,98,97,96,95,90,85,80,81,82,83,88,87,86,91,92,93,94,89,84,79,78,77,76,51,
	52,53,54,59,64,69,68,67,66,61,62,63,58,57,56,55,60,65,70,71,72,73,48,47,46,45,40,		52,53,54,59,64,69,68,67,66,61,62,63,58,57,56,55,60,65,70,71,72,73,48,47,46,45,40,

imported>Gfis at 21:24, 24 August 2017

2017-08-24T21:24:40Z

← Older revision		Revision as of 21:24, 24 August 2017
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	* Symmetricy around n=12, a(12) = 2*(5<sup>1</sup> + 5<sup>0</sup>)		* Symmetricy around n=12, a(12) = 2*(5<sup>1</sup> + 5<sup>0</sup>)
	* Groups of length 5<sup>n</sup> - 1, n=0,1,2 ...		* Groups of length 5<sup>n</sup> - 1, n=0,1,2 ...

			In the following I will refer to ''generations'' which correspond to the powers of 5. Knuth's values are generation 2 and the first of geneartion3 (49).

	I wrote a Perl program which plots the values of b-files with SVG. The [http://www.teherba.org/images/0/03/A220952.orig.svg image] shows a slighty distorted "Z" shape with "handles" on the diagonal. The nodes' values are showed in base 5. With another Perl program I tried to generate the starting 26 values, and a continuation up to the next power of 5 (125). The program did maintain the conditions noted above, but returned ten thousands of "unpleasant solutions". The conditions seem not to be strong enough.		I wrote a Perl program which plots the values of b-files with SVG. The [http://www.teherba.org/images/0/03/A220952.orig.svg image] shows a slighty distorted "Z" shape with "handles" on the diagonal. The nodes' values are showed in base 5. With another Perl program I tried to generate the starting 26 values, and a continuation up to the next power of 5 (125). The program did maintain the conditions noted above, but returned ten thousands of "unpleasant solutions". The conditions seem not to be strong enough.
Line 55:		Line 57:

	===Explanation of Generation 3===		===Explanation of Generation 3===
	For the "Z"s on the main diagonal, the upper, horizontal stroke consists of 4 nodes spanning a length of 3*5<sup>n</sup>. Before that upper stroke and behind the lower stroke there is a "handle" consisting of the shape of generation 2 ~~(Knuth's values)~~. Whenever the generation 2 shape occurs again in the squence, it is mirrored on the vertical axis. Please note that the "shape" of generation 1 consists of the values 1,2,3 which are also visible - each time mirrored - on the "/"-stroke of generation 2.		For the "Z"s on the main diagonal, the upper, horizontal stroke consists of 4 nodes spanning a length of 3*5<sup>n</sup>. Before that upper stroke and behind the lower stroke there is a "handle" consisting of the shape of generation 2. Whenever the generation 2 shape occurs again in the squence, it is mirrored on the vertical axis. Please note that the "shape" of generation 1 consists of the values 1,2,3 which are also visible - each time mirrored - on the "/"-stroke of generation 2.

	Therefore I hope to be able to write a generating program for higher powers of 5. Bbut I have no idea for additional properties of this sequence.		Therefore I hope to be able to write a generating program for higher powers of 5. Bbut I have no idea for additional properties of this sequence.