A190278 Number of decimal digits in LCM of Fibonacci sequence {F_1, ..., F_n}.

1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 13, 15, 17, 20, 21, 25, 27, 29, 31, 36, 38, 42, 44, 48, 51, 56, 58, 64, 67, 72, 75, 80, 83, 90, 94, 99, 103, 111, 113, 122, 126, 131, 136, 145, 149, 157, 162, 168, 173, 184, 188, 196, 201, 209, 215

Offset: 1

Author

Jonathan Vos Post, May 07 2011

Keywords

• nonn
• base

Comments

Implicitly in Mathematics Teacher, Problem 15, pp. 684-685, May 2011.

Examples

			a(4) = 1 because lcm(F_1, F_2, F_3, F_4) = 6 has one decimal digit.
a(19) = 25 because lcm(F_1, ..., F_19) = 2679944489486672512824720 has 25 decimal digits.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000045, A035105, A055642.

Programs

Maple

with(combinat):
b:= proc(n) option remember;
      `if`(n=1, 1, ilcm(b(n-1), fibonacci(n)))
    end:
a:= n-> length(b(n)):
seq(a(n), n=1..80); # Alois P. Heinz, Jul 28 2011

Mathematica

Table[IntegerLength[LCM@@Fibonacci[Range[n]]],{n,60}] (* Harvey P. Dale, Jan 10 2025 *)

PARI

a(n) = #Str(lcm(vector(n, k, fibonacci(k)))); \\ Michel Marcus, Mar 13 2018

Formula

a(n) = A055642(A035105(n)) = floor(log_10(10*A035105(n))).