Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #13 Apr 22 2024 12:05:47
%S 1,0,1,1,2,1,2,1,3,1,3,2,5,3,5,4,4,1,4,3,7,4,7,5,10,5,10,7,15,10,15,
%T 11,5,1,5,4,9,5,9,6,13,6,13,9,20,13,20,15,17,7,17,12,27,17,27,20,37,
%U 22,37,27,52,37,52,41,6,1,6,5,11,6,11,7,16,7,16,11,25,16,25,19
%N a(n) = (-1)^n*a((n - 2^A007814(n))/2) + a(floor((2*n - 2^A007814(n))/2)) for n > 0 and a(0) = 1.
%C This sequence was originally introduced by _Mikhail Kurkov_ in A217924 where he conjectured that A217924(n) = Sum_{k=0..2^n-1} a(k).
%F Conjecture (by _Mikhail Kurkov_): a(2^n - 1) = A000296(n).
%F Conjecture (by _Mikhail Kurkov_): a((4^n - 1)/3) = A288268(n).
%p f := n -> padic[ordp](n, 2):
%p a := proc(n) option remember; if n = 0 then return 1 fi;
%p (-1)^n*a((n - 2^f(n))/2) + a(floor((2*n - 2^f(n))/2)) end:
%p seq(a(n), n = 0..79);
%Y Cf. A007814, A000296, A217924, A288268.
%K nonn
%O 0,5
%A _Peter Luschny_, Apr 22 2024