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a(n) = -1 + Product_{k=1..n} Fibonacci(k).
2

%I #20 Aug 29 2021 17:04:13

%S 0,0,1,5,29,239,3119,65519,2227679,122522399,10904493599,

%T 1570247078399,365867569267199,137932073613734399,

%U 84138564904377983999,83044763560621070207999,132622487406311849122175999,342696507457909818131702783999,1432814097681520949608649339903999

%N a(n) = -1 + Product_{k=1..n} Fibonacci(k).

%C a(n) asymptotic to Phi^A000217(n). Prime for n = 4, 5, 6, 7, 8, 14, 15. Semiprime for n = 9, 10, 11, 20.

%C Thus, it is not until the 12th element in the sequence that we get number with more than 2 prime factors: 1570247078399 = 37 * 59 * 16349 * 43997. - _Jonathan Vos Post_, Dec 08 2012

%H Harvey P. Dale, <a href="/A103815/b103815.txt">Table of n, a(n) for n = 1..99</a>

%F a(n) = Product[Fibonacci[k], {k, 1, n}]-1 = Product[A000045[k], {k, 1, n}]-1.

%F a(n) = A003266(n) - 1. - _Alois P. Heinz_, Aug 09 2018

%e a(15) = 1 * 1 * 2 * 3 * 5 * 8 * 13 * 21 * 34 * 55 * 89 * 144 * 233 * 377 * 610 - 1 = 84138564904377983999 is prime.

%p F:= n-> (<<0|1>, <1|1>>^n)[1, 2]:

%p a:= n-> -1 + mul(F(i), i=1..n):

%p seq(a(n), n=1..20); # _Alois P. Heinz_, Aug 09 2018

%t FoldList[Times,Fibonacci[Range[20]]]-1 (* _Harvey P. Dale_, Aug 29 2021 *)

%Y Cf. A000045, A000217, A003266, A052449, A053413, A053408.

%K easy,nonn

%O 1,4

%A _Jonathan Vos Post_, Mar 29 2005