A295907 - OEIS

%I #16 Dec 12 2017 00:27:07

%S 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,

%T 81,112,58,30,62,0,66,34,0,72,37,0,78,120,82,126,86,0,90,46,94,0,49,

%U 100,0,52,159,162,220,224,171,232,177,240,183,186,252,128,0

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

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

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

%H Rémy Sigrist, <a href="/A295907/a295907.png">Scatterplot of the first 2500000 terms</a>

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

%o (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)))

%Y Cf. A296099.

%K nonn,base

%O 1,2

%A _Rémy Sigrist_, Dec 05 2017