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Initial digit of Fibonacci number F(n) in base 60.
4

%I #23 Jan 12 2023 04:19:32

%S 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,

%T 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,

%U 4,7,12,20,33,53,1,2,3,6,9,16,25,42,1,1,2,4,7,12

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

%H Alois P. Heinz, <a href="/A261607/b261607.txt">Table of n, a(n) for n = 0..10000</a> (first 1001 terms from Reinhard Zumkeller)

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Sexagesimal.html">Sexagesimal</a>.

%H Wikipedia, <a href="http://www.wikipedia.org/wiki/Sexagesimal">Sexagesimal</a>.

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

%F 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

%t IntegerDigits[Fibonacci[Range[0, 75]], 60][[All, 1]] (* _Michael De Vlieger_, Jan 22 2022 *)

%o (Haskell)

%o a261607 = last . a261575_row

%o (PARI) a(n) = if (n, digits(fibonacci(n), 60)[1], 0); \\ _Michel Marcus_, Jan 22 2022

%Y Cf. A000045, A261575, A261585, A261606, A008963.

%K nonn,look,base

%O 0,4

%A _Reinhard Zumkeller_, Sep 09 2015