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

Author

Rémy Sigrist, Dec 05 2017

Keywords

• nonn
• base

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.

Examples

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

Links

• Rémy Sigrist, Scatterplot of the first 2500000 terms

Crossrefs

Cf. A296099.

Programs

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)))