OEIS/Attaching segments
Column 5
attach to: 3,7,11,15,19 ... => 3 mod 4 left side: 1,2,3,4,5,6 ... => 1 mod 1 remaining: 0,1,2 mod 4
Column 6
attach to: 1,5,9,13,17 ... => 1 mod 4 left side: 1,4,7,10,13 1 mod 3 remaining: 0,2 mod 4 double step: if 1 mod 3 = 3 mod 4: 7, 19,31 => 7 mod 12