A388653 Numbers k >= 0 such that the interval [A000217(k), A000217(k + 1)] contains at least one Fibonacci number (A000045).

0, 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 16, 21, 26, 34, 43, 56, 71, 90, 115, 147, 187, 238, 304, 386, 492, 626, 796, 1013, 1289, 1640, 2086, 2654, 3376, 4295, 5463, 6950, 8841, 11246, 14305, 18197, 23147, 29444, 37453, 47641, 60601, 77086, 98055, 124729, 158658

Offset

1,3

Comments

For k > 2, the number of the Fibonacci numbers on the interval [A000217(k), A000217(k + 1)] is 0 or 1.

Links

Table of n, a(n) for n=1..50.

Formula

For n >= 11, k = A057042(n) - 1.

Example

2 is a term since the interval [A000217(2), A000217(3)] = [3, 6] contains F_4 = 3 and F_5 = 5.
5 is a term since the interval [A000217(5), A000217(6)] = [15, 21] contains F_8 = 21.

Crossrefs

Cf. A000045, A000217, A039595, A057042.

Sequence in context: A087950 A060527 A152493 * A229028 A079002 A119984

Adjacent sequences: A388650 A388651 A388652 * A388654 A388655 A388656

Keyword

nonn

Author

Ctibor O. Zizka, Sep 19 2025

Status

approved