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A332586 a(n) = minimal value of n+k+1 such that the concatenation of the binary expansions of n,n+1,...,n+k is divisible by n+k+1, or -1 if no such n+k+1 exists. 3

%I

%S 3,9,257,165,29,13,585,23,11,15,395,21,1605,33,185,59,1897,229,77,41,

%T 91,1377,37,111,251,1559,605,329,43,61,6451,345,30673,47,187,45,127,

%U 2759,69,5871,43,1493,239,523,101,166575,175,1123,3609,303,93,1139465,4495201

%N a(n) = minimal value of n+k+1 such that the concatenation of the binary expansions of n,n+1,...,n+k is divisible by n+k+1, or -1 if no such n+k+1 exists.

%C For n up to 128 the presently unknown values are a(52) and a(53). If these values of k exist, they are at least 1000000.

%H Michael S. Branicky, <a href="/A332586/b332586.txt">Table of n, a(n) for n = 1..137</a>

%H Michael S. Branicky, <a href="/A332586/a332586_2.txt">Table of n, a(n) for n = 1..332</a>, with -1 if k is presently unknown (the current search limit is 2000000). Note that this does not mean that a(n) = -1.

%H J. S. Myers, R. Schroeppel, S. R. Shannon, N. J. A. Sloane, and P. Zimmermann, <a href="http://arxiv.org/abs/2004.14000">Three Cousins of Recaman's Sequence</a>, arXiv:2004:14000 [math.NT], April 2020.

%H Scott R. Shannon, <a href="/A332586/a332586.txt">Table of n, a(n) for n = 1..128</a>, with -1 if k is presently unknown (the current search limit is 1000000). Note that this does not mean that a(n) = -1.

%H Scott R. Shannon, <a href="/A332586/a332586_1.txt">The quotient after the final division, for n = 1..15</a>

%t Table[k=0;While[Mod[FromDigits[Flatten@IntegerDigits[Range[n,n+ ++k],2],2],n+k+1]!=0];n+k+1,{n,20}] (* _Giorgos Kalogeropoulos_, Apr 27 2021 *)

%Y Cf. A332580, A332584, A332563.

%K sign,base

%O 1,1

%A _Scott R. Shannon_ and _N. J. A. Sloane_, Feb 25 2020

%E a(52) from _Michael S. Branicky_, Apr 25 2021

%E a(53) from _Michael S. Branicky_, Apr 28 2021

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Last modified June 12 10:29 EDT 2021. Contains 344946 sequences. (Running on oeis4.)