

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



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
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OFFSET

1,1


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


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 *)


CROSSREFS

Cf. A332580, A332584, A332563.
Sequence in context: A091409 A027891 A073889 * A211898 A318970 A132516
Adjacent sequences: A332583 A332584 A332585 * A332587 A332588 A332589


KEYWORD

sign,base,changed


AUTHOR

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


EXTENSIONS

a(52) from Michael S. Branicky, Apr 25 2021
a(53) from Michael S. Branicky, Apr 28 2021


STATUS

approved



