A332563 a(n) = minimal positive k 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 k exists.

1, 6, 253, 160, 23, 6, 577, 14, 1, 4, 383, 8, 1591, 18, 169, 42, 1879, 210, 57, 20, 69, 1354, 13, 86, 225, 1532, 577, 300, 13, 30, 6419, 312, 30639, 12, 151, 8, 89, 2720, 29, 5830, 1, 1450, 195, 478, 55, 166528, 127, 1074, 3559, 252, 41

Offset: 1

Author

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

Keywords

• sign
• base

Comments

A base 2 analog of A332580.

For n up to 1000 the presently unknown values are a(213) and a(743).

Links

• Joseph Myers, Table of n, a(n) for n = 1..212
• Joseph Myers, Table of n, a(n) for n = 1..1024. The UNKNOWN entries at n = 213 and 743 are either -1 or greater than 10^9. [This extends an earlier table of Scott R. Shannon, which searched up to 128 with a search limit of 10^6.]
• 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, The quotient after the final division, for n = 1..15
• 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).

Crossrefs

Cf. A332580, A332584, A332586.