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%I #8 Feb 05 2020 16:53:49
%S 1,0,0,0,0,1,0,0,0,4,1,2,0,-1,0,-1,0,9,4,4,1,10,2,2,0,5,-1,1,0,1,-1,0,
%T 0,16,9,34,4,23,4,37,1,5,10,10,2,14,2,4,0,7,5,11,-1,5,1,6,0,-4,1,0,-1,
%U -3,0,-1,0,57,16,116,9,98,34,84,4,69,23,103,4,9,37,98,1,52,5,70,10,19,10,39,2,19,14,38,2,34,4,18,0,39
%N a(n) = A002487(A163511(n)) - A002487(n).
%H Antti Karttunen, <a href="/A331749/b331749.txt">Table of n, a(n) for n = 0..16384</a>
%H Antti Karttunen, <a href="/A331749/a331749.txt">Data supplement: n, a(n) computed for n = 0..65537</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) = A323901(n) - A002487(n) = A002487(A163511(n)) - A002487(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 A331749(n) = (A002487(A163511(n)) - A002487(n));
%Y Cf. A002487, A163511, A323901, A331743, A331748.
%K sign
%O 0,10
%A _Antti Karttunen_, Feb 05 2020
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