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==''The On-Line Encyclopedia of Integer | ==''[http://oeis.org The On-Line Encyclopedia of Integer Sequences]®'' of Neil Sloane et al.== | ||
* ''A Handbook of Integer Sequences'' | * ''A Handbook of Integer Sequences'', N. J. A. Sloane, Academic Press, New York and London, 1973. | ||
* | * ''[https://oeis.org/wiki/The_Encyclopedia_of_Integer_Sequences The_Encyclopedia_of_Integer_Sequences]'', N. J. A. Sloane and S. Plouffe, Academic Press, San Diego, 1995, 587 pp. ISBN 0-12-558630-2. | ||
===Groups of sequences implemented for [https://github.com/archmageirvine/joeis jOEIS]=== | |||
* '''[[OEIS/morfix|morfix]]''', fixed points of morphisms | |||
* '''[[OEIS/squaredig|squaredig]]''', numbers which have a subset of digits in the number and its square | |||
===Small projects=== | |||
Cf. my [https://oeis.org/wiki/User:Georg_Fischer OEIS wiki user page] | |||
* '''[[OEIS/coors|Coordination sequences for k-uniform tilings]]''' of Brian Galebach | |||
* '''[[OEIS/B-file_check|B-file check]]''', initiated by Martin Pedersen | |||
* '''[[OEIS/Broken_Links|Broken links]]''' detection and repair | |||
* '''[https://oeis.org/wiki/User:Georg_Fischer/Coincidences Coincidences]''' - search lists for sequences with common terms | |||
* '''[[OEIS/DFSA|DFSA]] Deterministic finite state automata for the enumeration of arrays with conditions | |||
* '''[http://www.teherba.org/trottermath.net WTM]''' World of Terrel Trotter's Math (archive copy of the original webpage of 2004, c.f. his [https://oeis.org/wiki/User:Terrel_Trotter,_Jr. OEIS user page]) | |||
* '''[[OEIS/Engel_expansion|Engel expansion]]''' - English translation of Friedrich Engel's speech: ''Entwicklung der Zahlen nach Stammbrüchen.'' Verhandlungen der 52. | |||
* '''[[OEIS/Eta_products|Eta products]]''' Dedekind eta, Jacobi theta_m, Ramanujan phi, psi, chi, f, a | |||
* '''[[OEIS/Generating_Functions_and_Recurrences|Generating Functions and Recurrences]]''' | |||
* '''[[OEIS/Holonomic_Project|Holonomic Project]]''' | |||
* '''[[OEIS/Infinite_Products|Infinite Products]]''' | |||
* '''[[OEIS/A220952|A220952]]''': 0, 1, 2, 3, 4, 9, 14, 19, 18, 17, 16, 11, 12, 13, ..., 49 ... by Donald E. Knuth, Feb. 20, 2013, was <code>unkn</code>, with additional '''[[OEIS/FASS_curves|FASS curves]]''': space-'''f'''illing, self-'''a'''voiding, '''s'''imple and self-'''s'''imilar curves | |||
* '''[https://oeis.org/A131388 A131388]''', and [https://oeis.org/A131393 A131393] with recovered ''Rule 2'' and generalized '''[[OEIS/Negative-Positive|negative-positive]]''' incrementing sequences of Clark Kimberling, with listing and program | |||
* '''[http://oeis.org/A030707 A030707]''', '''[http://oeis.org/A055187 A055187]''', '''[http://oeis.org/A217760 A217760]''' and related sequences, listing and program for generalized '''[[OEIS/Cumulative_counting|cumulative counting]]''', Clark Kimberling's [http://faculty.evansville.edu/ck6/integer/unsolved.html problem no. 4] | |||
* '''[[OEIS/Triangles|Triangles with interlacing rows]]''', Clark Kimberling's [http://faculty.evansville.edu/ck6/integer/unsolved.html problem no. 18]; Perl and C programs find 1, 2, 20, 1744, 2 002 568, 42 263 042 752 triangles for the ''between'' condition | |||
=== | ===Individual sequences=== | ||
* '''[[OEIS/ | * '''[[OEIS/A003828|A003828]]''', Numbers n such that n^4 is a primitive sum of 3 positive fourth powers: 422481, 2813001, 8707481, 12197457, 16003017, 16430513, 20615673, 44310257, 68711097, 117112081, 145087793, 156646737, 589845921, 638523249, 873822121, 1259768473, 1679142729, 1787882337, 1871713857 | ||
* '''[https://oeis.org/A035505 A035505]''', Kimberling's expulsion (shuffle) array [http://www.teherba.org/fasces/oeis/kea.html array visualization] | |||
* '''[[OEIS/A070080|A070080]]''', Triangles with integer sides, areas and in-radii | |||
* '''[https://oeis.org/A070165 A070165]''', Collatz conjecture: '''[[OEIS/3x%2B1_Problem]]''' (solution proposal) | |||
* '''[http://oeis.org/A112273 A112273]''': 5, 15, 365, 945 - a puzzle sequence | |||
** my guess: 5*3^0, 5*3^1, 5*73 (or should that be 315 = 5*7*3^2 ?), 5*7*3^3 | |||
* '''[https://oeis.org/A213457 A213457]''' Intertwining numbers: a(8) = 1058349286 | |||
* '''[[OEIS/A291939|A291939]]''': 1, 12, 19, 27, 37 - overlapping of Collatz sequences, was <code>unkn</code>, with 3D visualization | |||
===Index sections=== | |||
* [https://oeis.org/wiki/Index_to_OEIS:_Section_Rec Index of linear recurrences with constant coefficients], mechanically generated every 3rd month | |||
* [https://oeis.org/w/index.php?title=Index_to_OEIS:_Sums_of_like_powers Index to OEIS: Sums of like powers] 2020-08-04 | |||
* [[OEIS/Wikipedia index]] | |||
Latest revision as of 08:47, 6 April 2024
The On-Line Encyclopedia of Integer Sequences® of Neil Sloane et al.
- A Handbook of Integer Sequences, N. J. A. Sloane, Academic Press, New York and London, 1973.
- The_Encyclopedia_of_Integer_Sequences, N. J. A. Sloane and S. Plouffe, Academic Press, San Diego, 1995, 587 pp. ISBN 0-12-558630-2.
Groups of sequences implemented for jOEIS
- morfix, fixed points of morphisms
- squaredig, numbers which have a subset of digits in the number and its square
Small projects
Cf. my OEIS wiki user page
- Coordination sequences for k-uniform tilings of Brian Galebach
- B-file check, initiated by Martin Pedersen
- Broken links detection and repair
- Coincidences - search lists for sequences with common terms
- DFSA Deterministic finite state automata for the enumeration of arrays with conditions
- WTM World of Terrel Trotter's Math (archive copy of the original webpage of 2004, c.f. his OEIS user page)
- Engel expansion - English translation of Friedrich Engel's speech: Entwicklung der Zahlen nach Stammbrüchen. Verhandlungen der 52.
- Eta products Dedekind eta, Jacobi theta_m, Ramanujan phi, psi, chi, f, a
- Generating Functions and Recurrences
- Holonomic Project
- Infinite Products
- A220952: 0, 1, 2, 3, 4, 9, 14, 19, 18, 17, 16, 11, 12, 13, ..., 49 ... by Donald E. Knuth, Feb. 20, 2013, was
unkn, with additional FASS curves: space-filling, self-avoiding, simple and self-similar curves - A131388, and A131393 with recovered Rule 2 and generalized negative-positive incrementing sequences of Clark Kimberling, with listing and program
- A030707, A055187, A217760 and related sequences, listing and program for generalized cumulative counting, Clark Kimberling's problem no. 4
- Triangles with interlacing rows, Clark Kimberling's problem no. 18; Perl and C programs find 1, 2, 20, 1744, 2 002 568, 42 263 042 752 triangles for the between condition
Individual sequences
- A003828, Numbers n such that n^4 is a primitive sum of 3 positive fourth powers: 422481, 2813001, 8707481, 12197457, 16003017, 16430513, 20615673, 44310257, 68711097, 117112081, 145087793, 156646737, 589845921, 638523249, 873822121, 1259768473, 1679142729, 1787882337, 1871713857
- A035505, Kimberling's expulsion (shuffle) array array visualization
- A070080, Triangles with integer sides, areas and in-radii
- A070165, Collatz conjecture: OEIS/3x+1_Problem (solution proposal)
- A112273: 5, 15, 365, 945 - a puzzle sequence
- my guess: 5*3^0, 5*3^1, 5*73 (or should that be 315 = 5*7*3^2 ?), 5*7*3^3
- A213457 Intertwining numbers: a(8) = 1058349286
- A291939: 1, 12, 19, 27, 37 - overlapping of Collatz sequences, was
unkn, with 3D visualization
Index sections
- Index of linear recurrences with constant coefficients, mechanically generated every 3rd month
- Index to OEIS: Sums of like powers 2020-08-04
- OEIS/Wikipedia index