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

%I A190278 #21 Jan 10 2025 15:04:05
%S A190278 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 A190278 48,51,56,58,64,67,72,75,80,83,90,94,99,103,111,113,122,126,131,136,
%U A190278 145,149,157,162,168,173,184,188,196,201,209,215
%N A190278 Number of decimal digits in LCM of Fibonacci sequence {F_1, ..., F_n}.
%C A190278 Implicitly in Mathematics Teacher, Problem 15, pp. 684-685, May 2011.
%H A190278 Charles R Greathouse IV, <a href="/A190278/b190278.txt">Table of n, a(n) for n = 1..10000</a>
%F A190278 a(n) = A055642(A035105(n)) = floor(log_10(10*A035105(n))).
%e A190278 a(4) = 1 because lcm(F_1, F_2, F_3, F_4) = 6 has one decimal digit.
%e A190278 a(19) = 25 because lcm(F_1, ..., F_19) = 2679944489486672512824720 has 25 decimal digits.
%p A190278 with(combinat):
%p A190278 b:= proc(n) option remember;
%p A190278       `if`(n=1, 1, ilcm(b(n-1), fibonacci(n)))
%p A190278     end:
%p A190278 a:= n-> length(b(n)):
%p A190278 seq(a(n), n=1..80); # _Alois P. Heinz_, Jul 28 2011
%t A190278 Table[IntegerLength[LCM@@Fibonacci[Range[n]]],{n,60}] (* _Harvey P. Dale_, Jan 10 2025 *)
%o A190278 (PARI) a(n) = #Str(lcm(vector(n, k, fibonacci(k)))); \\ _Michel Marcus_, Mar 13 2018
%Y A190278 Cf. A000045, A035105, A055642.
%K A190278 nonn,base
%O A190278 1,5
%A A190278 _Jonathan Vos Post_, May 07 2011