A256654 Least Fibonacci number not less than n.

1, 2, 3, 5, 5, 8, 8, 8, 13, 13, 13, 13, 13, 21, 21, 21, 21, 21, 21, 21, 21, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89

Offset: 1

Author

Clark Kimberling, Apr 08 2015

Keywords

• nonn
• easy

Comments

This sequence plays a role in the definition of minimal alternating Fibonacci representations, introduced at A256655.

Essentially the same as A246104. - R. J. Mathar, Apr 14 2015

Links

• Clark Kimberling, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000045, A087172, A246104, A256655.

Programs

Mathematica

h[0] = {1}; h[n_] := Join[h[n - 1], Table[Fibonacci[n + 2], {k, 1, Fibonacci[n]}]]; h[10]

Formula

Concatenate these numbers: F(2), F(3), F(4), then F(3) F(5)'s, then F(4) F(6)'s, then F(5) F(7)'s, ... F(n+2) F(n)'s, ..., where F = A000045, the Fibonacci numbers.

Sum_{n>=1} 1/a(n)^2 = 1 + Sum_{n>=1} F(n)/F(n+2)^2 = 1.5651369873... . - Amiram Eldar, Aug 16 2022