A331748 a(n) = A002487(n) XOR A002487(A163511(n)).

1, 0, 0, 0, 0, 7, 0, 0, 0, 12, 7, 2, 0, 1, 0, 7, 0, 11, 12, 12, 7, 26, 2, 14, 0, 11, 1, 1, 0, 15, 7, 0, 0, 16, 11, 34, 12, 41, 12, 37, 7, 27, 26, 26, 2, 22, 14, 4, 0, 25, 11, 27, 1, 31, 1, 26, 0, 12, 15, 0, 7, 15, 0, 3, 0, 71, 16, 116, 11, 126, 34, 108, 12, 91, 41, 107, 12, 11, 37, 98, 7, 76, 27, 74, 26, 61, 26, 43, 2, 53, 22, 42, 14, 34, 4, 22, 0, 57

Offset: 0

Author

Antti Karttunen, Feb 05 2020

Keywords

• nonn
• base

Links

• Antti Karttunen, Table of n, a(n) for n = 0..65536
• Index entries for sequences related to binary expansion of n
• Index entries for sequences related to Stern's sequences

Crossrefs

Cf. A002487, A003987, A163511, A323901, A331743, A331749.

Programs

PARI

A002487(n) = { my(a=1, b=0); while(n>0, if(bitand(n, 1), b+=a, a+=b); n>>=1); (b); }; \\ From A002487
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t }; \\ From A005940
A054429(n) = ((3<<#binary(n\2))-n-1); \\ From A054429
A163511(n) = if(!n,1,A005940(1+A054429(n)));
A331748(n) = bitxor(A002487(A163511(n)), A002487(n));

Formula

a(n) = A002487(n) XOR A323901(n) = A002487(n) XOR A002487(A163511(n)).

a(2^n) = 0 for all n >= 0.