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

1,1

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).

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}]]

Crossrefs

Cf. A332580, A332563.

Sequence in context: A179480 A245326 A241534 * A035050 A198790 A306995

Adjacent sequences: A337134 A337135 A337136 * A337138 A337139 A337140

Keyword

nonn,look,base

Author

Olivier Gérard, Sep 14 2020

Status

approved