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A357589 a(n) = n - A130312(n).

%I A357589 #21 Jun 21 2024 15:23:42
%S A357589 0,1,1,2,2,3,4,3,4,5,6,7,5,6,7,8,9,10,11,12,8,9,10,11,12,13,14,15,16,
%T A357589 17,18,19,20,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,
%U A357589 32,33,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36
%N A357589 a(n) = n - A130312(n).
%F A357589 Conjecture: a(n) = 2*n - 1 - A183544(n).
%o A357589 (PARI) b1(n)=local(m); if(n<1, 0, m=0; until(fibonacci(m)>n, m++); m-2) \\ A072649
%o A357589 a(n)=n - fibonacci(b1(n))
%o A357589 (Python)
%o A357589 from itertools import islice
%o A357589 def A357589_gen(): # generator of terms
%o A357589     a, b, i = 1, 1, 1
%o A357589     while True:
%o A357589         yield from (j-a for j in range(i,i+a))
%o A357589         i += a
%o A357589         a, b = b, a+b
%o A357589 A357589_list = list(islice(A357589_gen(),30)) # _Chai Wah Wu_, Oct 13 2022
%Y A357589 Cf. A130312, A183544.
%K A357589 nonn,easy
%O A357589 1,4
%A A357589 _Mikhail Kurkov_, Oct 05 2022