A261585 Number of sexagesimal digits of Fibonacci numbers in base-60 representation.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10

Offset: 0

Author

Reinhard Zumkeller, Sep 09 2015

Keywords

• nonn
• base

Comments

a(n) = length of n-th row in table A261575.

a(n)/n tends towards log_60(phi) = 0.117530856953191562796405213751... - Hans J. H. Tuenter, Jul 13 2025

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
• Eric Weisstein's World of Mathematics, Sexagesimal
• Wikipedia, Sexagesimal

Crossrefs

Cf. A261575, A000045, A001622, A060384.

Programs

Haskell

a261585 = length . a261575_row

Mathematica

Join[{1}, IntegerLength[Fibonacci[Range[100]], 60]] (* Paolo Xausa, Feb 19 2024 *)

Formula

For n>1, a(n) = 1+floor(n*log_60(phi)-log_60(5)/2), where phi=(1+sqrt(5))/2, the golden ratio. - Hans J. H. Tuenter, Jul 13 2025.