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).

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, 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, 36, 14, 15, 17, 16, 20, 18, 17, 24, 20, 21, 19, 18, 29, 13, 14, 16

Offset: 0

Author

Rémy Sigrist, Jan 31 2023

Keywords

• nonn
• look

Comments

See A095791 for the corresponding k's.

This sequence has similarities with A227192; here we use Fibonacci numbers, there powers of 2.

Examples

			The first terms, alongside the corresponding k's, are:
  n      a(n)  k
  -----  ----  ---
      0     0  N/A
      1     1    1
      2     3    2
      3     2    2
      4     6    3
      5     4    3
      6     3    3
      7    10    4
      8     6    4
      9     7    4
     10     5    4
     11     4    4
     12    15    5
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10946

Crossrefs

See A095791, A360260 and A360265 for similar sequences.

Cf. A000045, A001911, A227192.

Programs

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]));); }

Formula

a(A001911(n)) = n.