A261607 Initial digit of Fibonacci number F(n) in base 60.

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 1, 2, 3, 6, 10, 16, 26, 43, 1, 1, 3, 4, 7, 12, 20, 33, 54, 1, 2, 3, 6, 10, 16, 26, 42, 1, 1, 3, 4, 7, 12, 20, 33, 54, 1, 2, 3, 6, 10, 16, 26, 42, 1, 1, 2, 4, 7, 12, 20, 33, 53, 1, 2, 3, 6, 9, 16, 25, 42, 1, 1, 2, 4, 7, 12

Offset: 0

Author

Reinhard Zumkeller, Sep 09 2015

Keywords

• nonn
• look
• base
• changed

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000 (first 1001 terms from Reinhard Zumkeller)
• Eric Weisstein's World of Mathematics, Sexagesimal.
• Wikipedia, Sexagesimal.

Crossrefs

Cf. A000045, A261575, A261585, A261606, A008963, A001622.

Programs

Haskell

a261607 = last . a261575_row

Mathematica

IntegerDigits[Fibonacci[Range[0, 75]], 60][[All, 1]] (* Michael De Vlieger, Jan 22 2022 *)

PARI

a(n) = if (n, digits(fibonacci(n), 60)[1], 0); \\ Michel Marcus, Jan 22 2022

Formula

a(n) = A261575(n, A261585(n)-1).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{d=1..59} d*log(1+1/d)/log(60) = 13.92958... . - Amiram Eldar, Jan 12 2023

For n>9, a(n) = floor(60^{alpha*n-beta}), where alpha=log_60(phi), beta=log_60(5)/2, {x}=x-floor(x) denotes the fractional part of x, and phi = (1+sqrt(5))/2 = A001622. - Hans J. H. Tuenter, Aug 26 2025