

A337137


Variant of A332563  binary version of Recamán concatenation sequence.


1



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, 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, 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
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OFFSET

1,1


COMMENTS

Inspired by Neil Sloane's presentation at Rutgers' Experimental Mathematics Seminar (see the Links section).
In the original version (A332563), for a given n, one concatenate the binary representation of nn+1n+2...n+i until the corresponding number is divisible by n+i+1.
In this variant, one skips n+1 as an ingredient of the concatenation.
A337137(n) records the least i such that nn+2n+3...n+i is divisible by n+i+1.
This version is tamer than the one in A332563.
The scatterplot graph shows some interesting structures.


LINKS



MATHEMATICA

Module[{s, i, imax = 128},
Table[ s = IntegerDigits[n, 2]; i = 0;
While[Mod[FromDigits[s, 2], n + i + 1] > 0 && i <= imax, i = i + 1;
s = Join[s, IntegerDigits[n + i + 1, 2]]];
i /. {imax + 1 > Infinity} , {n, 1, 127}]]


CROSSREFS



KEYWORD



AUTHOR



STATUS

approved



