A337137 Variant of A332563 - binary version of Recamán concatenation sequence.

2, 1, 3, 3, 2, 1, 8, 4, 6, 3, 2, 3, 2, 1, 3, 15, 10, 13, 4, 3, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 8, 7, 27, 29, 28, 27, 26, 10, 24, 23, 22, 21, 20, 19, 3, 15, 14, 15, 14, 13, 12, 3, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 16, 15, 62, 13, 2, 27, 58, 16, 15, 55, 22, 2, 52, 51, 2, 36, 16, 3, 46, 33, 7, 43, 2, 5, 3, 23, 38, 33, 4, 3, 34, 33, 13, 7, 22, 29, 16, 3, 26, 22, 16, 7, 22, 17, 2, 3, 2, 17, 16, 9, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 128

Offset: 1

Author

Olivier Gérard, Sep 14 2020

Keywords

• nonn
• look
• base

Comments

Inspired by Neil Sloane's presentation at Rutgers' Experimental Mathematics Seminar (see the Links section).

In the original version (A332563), for a given n, one concatenate the binary representation of n||n+1||n+2||...||n+i until the corresponding number is divisible by n+i+1.

In this variant, one skips n+1 as an ingredient of the concatenation.

A337137(n) records the least i such that n||n+2||n+3||...||n+i is divisible by n+i+1.

This version is tamer than the one in A332563.

The scatterplot graph shows some interesting structures.

Links

• Olivier Gérard, Table of n, a(n) for n = 1..2048
• N. J. A. Sloane, Conant's Gasket, Recamán Variations, the Enots Wolley Sequence, and Stained Glass Windows, Experimental Math Seminar, Rutgers University, Sep 10 2020 (video of Zoom talk).

Crossrefs

Cf. A332580, A332563.

Programs

Mathematica

Module[{s, i, imax = 128},
Table[ s = IntegerDigits[n, 2]; i = 0;
  While[Mod[FromDigits[s, 2], n + i + 1] > 0 && i <= imax, i = i + 1;
   s = Join[s, IntegerDigits[n + i + 1, 2]]];
  i /. {imax + 1 -> Infinity} , {n, 1, 127}]]