cp's OEIS Frontend

A360259 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).

%I A360259 #13 Feb 02 2023 14:44:23
%S A360259 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 A360259 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 A360259 36,14,15,17,16,20,18,17,24,20,21,19,18,29,13,14,16
%N A360259 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 A360259 See A095791 for the corresponding k's.
%C A360259 This sequence has similarities with A227192; here we use Fibonacci numbers, there powers of 2.
%H A360259 Rémy Sigrist, <a href="/A360259/b360259.txt">Table of n, a(n) for n = 0..10946</a>
%F A360259 a(A001911(n)) = n.
%e A360259 The first terms, alongside the corresponding k's, are:
%e A360259   n      a(n)  k
%e A360259   -----  ----  ---
%e A360259       0     0  N/A
%e A360259       1     1    1
%e A360259       2     3    2
%e A360259       3     2    2
%e A360259       4     6    3
%e A360259       5     4    3
%e A360259       6     3    3
%e A360259       7    10    4
%e A360259       8     6    4
%e A360259       9     7    4
%e A360259      10     5    4
%e A360259      11     4    4
%e A360259      12    15    5
%o A360259 (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 A360259 See A095791, A360260 and A360265 for similar sequences.
%Y A360259 Cf. A000045, A001911, A227192.
%K A360259 nonn,look
%O A360259 0,3
%A A360259 _Rémy Sigrist_, Jan 31 2023