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

%I A337137 #48 Jan 09 2021 21:05:34
%S A337137 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,
%T A337137 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,
%U A337137 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
%N A337137 Variant of A332563 - binary version of Recamán concatenation sequence.
%C A337137 Inspired by Neil Sloane's presentation at Rutgers' Experimental Mathematics Seminar (see the Links section).
%C A337137 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.
%C A337137 In this variant, one skips n+1 as an ingredient of the concatenation.
%C A337137 A337137(n) records the least i such that n||n+2||n+3||...||n+i is divisible by n+i+1.
%C A337137 This version is tamer than the one in A332563.
%C A337137 The scatterplot graph shows some interesting structures.
%H A337137 Olivier Gérard, <a href="/A337137/b337137.txt">Table of n, a(n) for n = 1..2048</a>
%H A337137 N. J. A. Sloane, <a href="https://vimeo.com/457349959">Conant's Gasket, Recamán Variations, the Enots Wolley Sequence, and Stained Glass Windows</a>, Experimental Math Seminar, Rutgers University, Sep 10 2020 (video of Zoom talk).
%t A337137 Module[{s, i, imax = 128},
%t A337137 Table[ s = IntegerDigits[n, 2]; i = 0;
%t A337137   While[Mod[FromDigits[s, 2], n + i + 1] > 0 && i <= imax, i = i + 1;
%t A337137    s = Join[s, IntegerDigits[n + i + 1, 2]]];
%t A337137   i /. {imax + 1 -> Infinity} , {n, 1, 127}]]
%Y A337137 Cf. A332580, A332563.
%K A337137 nonn,look,base
%O A337137 1,1
%A A337137 _Olivier Gérard_, Sep 14 2020