A331748 - OEIS

%I #6 Feb 05 2020 16:53:42

%S 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,

%T 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,

%U 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

%N a(n) = A002487(n) XOR A002487(A163511(n)).

%H Antti Karttunen, <a href="/A331748/b331748.txt">Table of n, a(n) for n = 0..65536</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%H <a href="/index/St#Stern">Index entries for sequences related to Stern's sequences</a>

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

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

%o (PARI)

%o A002487(n) = { my(a=1, b=0); while(n>0, if(bitand(n, 1), b+=a, a+=b); n>>=1); (b); }; \\ From A002487

%o A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t }; \\ From A005940

%o A054429(n) = ((3<<#binary(n\2))-n-1); \\ From A054429

%o A163511(n) = if(!n,1,A005940(1+A054429(n)));

%o A331748(n) = bitxor(A002487(A163511(n)), A002487(n));

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

%K nonn,base

%O 0,6

%A _Antti Karttunen_, Feb 05 2020