cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A053408 Numbers k such that A003266(k) + 1 is prime.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 22, 28
Offset: 1

Views

Author

G. L. Honaker, Jr., Jan 08 2000

Keywords

Comments

Next term > 300. - Joerg Arndt, Aug 16 2014
The corresponding primes are given in A053413. - Joerg Arndt, Aug 17 2014
If it exists, a(11) > 1100. - Robert Price, May 27 2019

Crossrefs

Programs

  • Mathematica
    Select[Range[30], PrimeQ[Fibonorial[#] + 1] &] (* Robert Price, May 26 2019 *)
  • PARI
    ff(n)=prod(i=1, n, fibonacci(i));
    for(n=1,10^6, if(ispseudoprime(ff(n)+1), print1(n,", "))); \\ Joerg Arndt, Aug 16 2014

Extensions

Definition edited by Daniel Forgues, Nov 29 2009
Edited definition, Joerg Arndt, Aug 17 2014

A052449 a(n) = 1 + Product_{k=1..n} Fibonacci(k).

Original entry on oeis.org

2, 2, 3, 7, 31, 241, 3121, 65521, 2227681, 122522401, 10904493601, 1570247078401, 365867569267201, 137932073613734401, 84138564904377984001, 83044763560621070208001, 132622487406311849122176001, 342696507457909818131702784001
Offset: 1

Views

Author

Keywords

Comments

The first 8 terms are primes. - Jonathan Vos Post, Dec 08 2012
a(22) and a(28) are also primes. - Robert Israel, Jun 10 2015
There are no further primes up to a(300). - Harvey P. Dale, Feb 28 2023

Crossrefs

Programs

  • GAP
    List([1..20], n-> 1+Product([1..n], j-> Fibonacci(j)) ); # G. C. Greubel, Sep 26 2019
  • Magma
    [1+(&*[Fibonacci(j): j in [1..n]]): n in [1..20]]; // G. C. Greubel, Sep 26 2019
    
  • Maple
    seq(1+mul(combinat:-fibonacci(j),j=1..n), n=1..30); # Robert Israel, Jun 10 2015
  • Mathematica
    1 + Table[Times @@ Fibonacci[Range[n]], {n, 20}] (* T. D. Noe, Dec 29 2012 *)
    FoldList[Times,Fibonacci[Range[20]]]+1 (* Harvey P. Dale, Feb 28 2023 *)
  • PARI
    vector(20, n, 1+prod(j=1,n, fibonacci(j))) \\ G. C. Greubel, Sep 26 2019
    
  • Sage
    [1+product(fibonacci(j) for j in (1..n)) for n in (1..20)] # G. C. Greubel, Sep 26 2019
    

Formula

a(n) = A003266(n)+1. - Robert Israel, Jun 10 2015

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

Original entry on oeis.org

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

Views

Author

Jonathan Vos Post, Mar 29 2005

Keywords

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

Examples

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

Crossrefs

Programs

  • 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 *)

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
Showing 1-3 of 3 results.