A190278 - OEIS

%I #19 Mar 13 2018 04:07:12

%S 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,

%T 48,51,56,58,64,67,72,75,80,83,90,94,99,103,111,113,122,126,131,136,

%U 145,149,157,162,168,173,184,188,196,201,209,215

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

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

%H Charles R Greathouse IV, <a href="/A190278/b190278.txt">Table of n, a(n) for n = 1..10000</a>

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

%e a(4) = 1 because lcm(F_1, F_2, F_3, F_4) = 6 has one decimal digit.

%e a(19) = 25 because lcm(F_1, ..., F_19) = 2679944489486672512824720 has 25 decimal digits.

%p with(combinat):

%p b:= proc(n) option remember;

%p       `if`(n=1, 1, ilcm(b(n-1), fibonacci(n)))

%p     end:

%p a:= n-> length(b(n)):

%p seq(a(n), n=1..80); # _Alois P. Heinz_, Jul 28 2011

%o (PARI) a(n) = #Str(lcm(vector(n, k, fibonacci(k)))); \\ _Michel Marcus_, Mar 13 2018

%Y Cf. A000045, A035105, A055642.

%K nonn,base

%O 1,5

%A _Jonathan Vos Post_, May 07 2011