A295907 a(n) = SumXOR_{k=1..n} A296099(k), where SumXOR is the analog of summation under the binary XOR operation.

1, 2, 0, 4, 15, 6, 0, 8, 27, 30, 11, 12, 0, 14, 30, 0, 17, 54, 57, 20, 0, 22, 46, 0, 25, 78, 81, 112, 58, 30, 62, 0, 66, 34, 0, 72, 37, 0, 78, 120, 82, 126, 86, 0, 90, 46, 94, 0, 49, 100, 0, 52, 159, 162, 220, 224, 171, 232, 177, 240, 183, 186, 252, 128, 0

Offset

1,2

Comments

For any n > 0, a(n) is divisible by n.

For any n > 0, if a(n) = 0, then A296099(n+1) is a multiple of n+1.

Links

Table of n, a(n) for n=1..65.

Rémy Sigrist, Scatterplot of the first 2500000 terms

Example

a(3) = A296099(1) XOR A296099(2) XOR A296099(3) = 1 XOR 3 XOR 2 = 0.

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 (x ", "); break)))

Crossrefs

Cf. A296099.

Sequence in context: A343472 A214199 A320491 * A317364 A265664 A320490

Adjacent sequences: A295904 A295905 A295906 * A295908 A295909 A295910

Keyword

nonn,base

Author

Rémy Sigrist, Dec 05 2017

Status

approved