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%I #13 Feb 02 2023 14:44:23
%S 0,1,3,2,6,4,3,10,6,7,5,4,15,8,9,11,7,8,6,5,21,10,11,13,12,16,9,10,12,
%T 8,9,7,6,28,12,13,15,14,18,16,15,22,11,12,14,13,17,10,11,13,9,10,8,7,
%U 36,14,15,17,16,20,18,17,24,20,21,19,18,29,13,14,16
%N a(0) = 0, and for any n > 0, let k > 0 be as small as possible and such that F(2) + ... + F(1+k) >= n (where F(m) denotes A000045(m), the m-th Fibonacci number); a(n) = k + a(F(2) + ... + F(1+k) - n).
%C See A095791 for the corresponding k's.
%C This sequence has similarities with A227192; here we use Fibonacci numbers, there powers of 2.
%H Rémy Sigrist, <a href="/A360259/b360259.txt">Table of n, a(n) for n = 0..10946</a>
%F a(A001911(n)) = n.
%e The first terms, alongside the corresponding k's, are:
%e n a(n) k
%e ----- ---- ---
%e 0 0 N/A
%e 1 1 1
%e 2 3 2
%e 3 2 2
%e 4 6 3
%e 5 4 3
%e 6 3 3
%e 7 10 4
%e 8 6 4
%e 9 7 4
%e 10 5 4
%e 11 4 4
%e 12 15 5
%o (PARI) { t = k = 0; print1 (0); for (n = 1, #a = vector(70), if (n > t, t += fibonacci(1+k++);); print1 (", "a[n] = k+if (t==n, 0, a[t-n]));); }
%Y See A095791, A360260 and A360265 for similar sequences.
%Y Cf. A000045, A001911, A227192.
%K nonn,look
%O 0,3
%A _Rémy Sigrist_, Jan 31 2023
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