A370731 a(n) is the least k >= 0 such that F(k) AND n = n (where F(k) denotes A000045(k), the k-th Fibonacci number and AND denotes the bitwise AND operator).

0, 1, 3, 4, 5, 5, 10, 10, 6, 7, 16, 16, 7, 7, 22, 22, 8, 8, 10, 10, 8, 8, 10, 10, 11, 11, 16, 16, 17, 17, 46, 46, 9, 10, 9, 10, 10, 10, 10, 10, 13, 13, 22, 22, 17, 17, 22, 22, 10, 10, 10, 10, 10, 10, 10, 10, 14, 14, 64, 64, 17, 17, 94, 94, 11, 11, 15, 16, 19

Offset: 0

Author

Rémy Sigrist, Feb 28 2024

Keywords

• nonn
• base

Comments

This sequence is well defined (see Comments in A370730).

Links

• Paolo Xausa, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000045, A370730.

Programs

Mathematica

A370731[n_] := Block[{k = -1}, While[BitAnd[Fibonacci[++k], n] != n]; k];
Array[A370731, 100, 0] (* Paolo Xausa, Mar 01 2024 *)

PARI

a(n) = { for (k = 0, oo, if (bitand(fibonacci(k), n)==n, return (k););); }

Formula

a(A000045(k)) = k for any k != 2.