

A296099


Lexicographically earliest sequence of distinct positive terms such that, for any n > 0, SumXOR_{k=1..n} a(k) is divisible by n, where SumXOR is the analog of summation under the binary XOR operation.


2



1, 3, 2, 4, 11, 9, 6, 8, 19, 5, 21, 7, 12, 14, 16, 30, 17, 39, 15, 45, 20, 22, 56, 46, 25, 87, 31, 33, 74, 36, 32, 62, 66, 96, 34, 72, 109, 37, 78, 54, 42, 44, 40, 86, 90, 116, 112, 94, 49, 85, 100, 52, 171, 61, 126, 60, 75, 67, 89, 65, 71, 13, 70, 124, 128
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OFFSET

1,2


COMMENTS

The partial XOR sums are given by A295907.
This sequence is a "binary" variant of A019444.
This sequence has connections with A286681; graphically, both sequences have similar fractal features; in the scatterplot of the current sequence, the rays emerging from the origin correspond to the numerous terms a(n) that are multiples of n.


LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, Scatterplot of the first 2500000 terms


PROG

(PARI) s = 0; x = 0; for (n=1, 65, for (k=1, oo, if (!bittest(s, k) && (xx=bitxor(x, k))%n==0, x = xx; s += 2^k; print1 (k ", "); break)))


CROSSREFS

Cf. A019444, A286681, A295907.
Sequence in context: A265353 A266189 A277743 * A319103 A290333 A137824
Adjacent sequences: A296096 A296097 A296098 * A296100 A296101 A296102


KEYWORD

nonn,look,base


AUTHOR

Rémy Sigrist, Dec 04 2017


STATUS

approved



