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A337137
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Variant of A332563 - binary version of Recamán concatenation sequence.
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1
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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
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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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 n||n+1||n+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 n||n+2||n+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.
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LINKS
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MATHEMATICA
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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}]]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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