A103815 a(n) = -1 + Product_{k=1..n} Fibonacci(k).

0, 0, 1, 5, 29, 239, 3119, 65519, 2227679, 122522399, 10904493599, 1570247078399, 365867569267199, 137932073613734399, 84138564904377983999, 83044763560621070207999, 132622487406311849122175999, 342696507457909818131702783999, 1432814097681520949608649339903999

Offset

1,4

Comments

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

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

Links

Harvey P. Dale, Table of n, a(n) for n = 1..99

Formula

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

a(n) = A003266(n) - 1. - Alois P. Heinz, Aug 09 2018

Example

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

Maple

F:= n-> (<<0|1>, <1|1>>^n)[1, 2]:
a:= n-> -1 + mul(F(i), i=1..n):
seq(a(n), n=1..20);  # Alois P. Heinz, Aug 09 2018

Mathematica

FoldList[Times, Fibonacci[Range[20]]]-1 (* Harvey P. Dale, Aug 29 2021 *)

Crossrefs

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

Sequence in context: A087662 A113012 A000354 * A134752 A370768 A231712

Adjacent sequences: A103812 A103813 A103814 * A103816 A103817 A103818

Keyword

easy,nonn

Author

Jonathan Vos Post, Mar 29 2005

Status

approved