This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A372205 #13 Apr 22 2024 12:05:47
%S A372205 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 A372205 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 A372205 22,37,27,52,37,52,41,6,1,6,5,11,6,11,7,16,7,16,11,25,16,25,19
%N A372205 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 A372205 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 A372205 Conjecture (by _Mikhail Kurkov_): a(2^n - 1) = A000296(n).
%F A372205 Conjecture (by _Mikhail Kurkov_): a((4^n - 1)/3) = A288268(n).
%p A372205 f := n -> padic[ordp](n, 2):
%p A372205 a := proc(n) option remember; if n = 0 then return 1 fi;
%p A372205 (-1)^n*a((n - 2^f(n))/2) + a(floor((2*n - 2^f(n))/2)) end:
%p A372205 seq(a(n), n = 0..79);
%Y A372205 Cf. A007814, A000296, A217924, A288268.
%K A372205 nonn
%O A372205 0,5
%A A372205 _Peter Luschny_, Apr 22 2024