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, 9, 257, 165, 29, 13, 585, 23, 11, 15, 395, 21, 1605, 33, 185, 59, 1897, 229, 77, 41, 91, 1377, 37, 111, 251, 1559, 605, 329, 43, 61, 6451, 345, 30673, 47, 187, 45, 127, 2759, 69, 5871, 43, 1493, 239, 523, 101, 166575, 175, 1123, 3609, 303, 93, 1139465, 4495201

Offset: 1

Author

Scott R. Shannon and N. J. A. Sloane, Feb 25 2020

Keywords

• sign
• base

Comments

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.

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..137
• Michael S. Branicky, Table of n, a(n) for n = 1..332, with -1 if k is presently unknown (the current search limit is 2000000). Note that this does not mean that a(n) = -1.
• J. S. Myers, R. Schroeppel, S. R. Shannon, N. J. A. Sloane, and P. Zimmermann, Three Cousins of Recaman's Sequence, arXiv:2004:14000 [math.NT], April 2020.
• Scott R. Shannon, Table of n, a(n) for n = 1..128, with -1 if k is presently unknown (the current search limit is 1000000). Note that this does not mean that a(n) = -1.
• Scott R. Shannon, The quotient after the final division, for n = 1..15

Crossrefs

Cf. A332580, A332584, A332563.

Programs

Mathematica

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 *)

Extensions

a(52) from Michael S. Branicky, Apr 25 2021

a(53) from Michael S. Branicky, Apr 28 2021