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.

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

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: A371635 A368226 A277743 * A349853 A319103 A332647

Adjacent sequences: A296096 A296097 A296098 * A296100 A296101 A296102

Keyword

nonn,look,base

Author

Rémy Sigrist, Dec 04 2017

Status

approved