A343646 a(0) = 0, and for any n > 0 such that F(k) <= n < F(k+1) for some k > 1, a(n) = F(k) + a(F(k+1) - n - 1) (where F(k) = A000045(k) is the k-th Fibonacci number).

0, 1, 2, 4, 3, 7, 6, 5, 11, 12, 10, 9, 8, 18, 19, 20, 16, 17, 15, 14, 13, 29, 30, 31, 33, 32, 26, 27, 28, 24, 25, 23, 22, 21, 47, 48, 49, 51, 50, 54, 53, 52, 42, 43, 44, 46, 45, 39, 40, 41, 37, 38, 36, 35, 34, 76, 77, 78, 80, 79, 83, 82, 81, 87, 88, 86, 85, 84

Offset

0,3

Comments

This sequence is a permutation of the nonnegative integers with inverse A343647.

This sequence has similarities with A003188; here we use Fibonacci numbers, there powers of 2.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..10945

Index entries for sequences that are permutations of the natural numbers

Formula

a(n) < A000045(k) for any n < A000045(k).

Example

For n = 1:
- 1 <= 1 < 2,
- so a(1) = 1 + a(2-1-1) = 1 + 0 = 1.
For n = 6:
- 5 <= 6 < 8,
- so a(6) = 5 + a(8-6-1) = 5 + a(1) = 5 + 1 = 6.
For n = 14:
- 13 <= 14 < 21,
- so a(14) = 13 + a(21-14-1) = 13 + a(6) = 13 + 6 = 19.
For n = 40:
- 34 <= 40 < 55,
- so a(40) = 34 + a(55-40-1) = 34 + a(14) = 34 + 19 = 53.

Prog

(PARI) a(n) = { if (n==0, return (0), for (k=2, oo, if (fibonacci(k)<=n && n<fibonacci(k+1), return (fibonacci(k) + a(fibonacci(k+1)-n-1))))) }

Crossrefs

Cf. A000045, A003188, A343647 (inverse).

Sequence in context: A199535 A064274 A035513 * A191442 A191738 A343647

Adjacent sequences: A343643 A343644 A343645 * A343647 A343648 A343649

Keyword

nonn

Author

Rémy Sigrist, Apr 24 2021

Status

approved