A360259 - OEIS

%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