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 1-7 of 7 results.

A053412 n-th nonzero Fibonacci numbers arising in A053408.

Original entry on oeis.org

1, 1, 2, 3, 5, 8, 13, 21, 17711, 317811
Offset: 0

Views

Author

G. L. Honaker, Jr., Jan 09 2000

Keywords

Crossrefs

See A000045 for the Fibonacci numbers.

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

Eric W. Weisstein

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

Links

Crossrefs

Cf. A000045, A003266, A053413, A053408.

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

A053413 Primes of the form A003266(n) + 1.

Original entry on oeis.org

2, 2, 3, 7, 31, 241, 3121, 65521, 1879127177606120717127879344567470740879360001, 1419564463863171507576408104556964008024375775796704645430601388670976000001
Offset: 1

Views

Author

G. L. Honaker, Jr., Jan 09 2000

Keywords

Comments

The corresponding n are given in A053408. - Joerg Arndt, Aug 16 2014

Links

Crossrefs

Cf. A059709, A053408.

Programs

  • Mathematica
    Select[Rest[FoldList[Times,1,Fibonacci[Range[80]]]+1],PrimeQ] (* Harvey P. Dale, Apr 25 2012 *)

Extensions

Edited by Daniel Forgues, Nov 30 2009
One more term (a(10)) from Harvey P. Dale, Apr 25 2012
Edited definition, Joerg Arndt, Aug 17 2014

A059709 Numbers k such that A003266(k) - 1 is prime.

Original entry on oeis.org

4, 5, 6, 7, 8, 14, 15
Offset: 1

Views

Author

Robert G. Wilson v, Feb 07 2001

Keywords

Comments

The a(n)-th almost-Fibonorial number is prime.
If it exists, a(8) > 1300. - Michael S. Branicky, Aug 17 2024

Links

Crossrefs

Cf. A003266, A053408.

Programs

  • Mathematica
    a = 1; Do[ a = a*Fibonacci[n]; If[ PrimeQ[a - 1], Print[n] ], {n, 1, 247} ]

Extensions

Definition corrected by Daniel Forgues, Nov 29 2009
Name edited by Michel Marcus, Jan 17 2024

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.

Links

Crossrefs

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

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

A240963 Numbers n such that the decimal expansion of n^n contains no zeros.

Original entry on oeis.org

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

Views

Author

Anthony Sand, Aug 05 2014

Keywords

Comments

A240962(a(n)) = 0.
The sequence seems to be finite; compare A007377 (n such that 2^n contains no 0).
For no reason I can fathom this is a subsequence of A053408. - Charles R Greathouse IV, Aug 21 2014

Examples

			1^1 = 1
2^2 = 4
3^3 = 27
4^4 = 256
5^5 = 3125
6^6 = 46656
7^7 = 823543
8^8 = 16777216
22^22 = 341427877364219557396646723584

Crossrefs

Cf. A240962, A007377, A030700, A053408.

Programs

  • Mathematica
    Select[Range[10^4], If[Count[IntegerDigits[#^#], 0] == 0, True] &] (* Michael De Vlieger, Aug 07 2014 *)
  • PARI
    for(n=1,10^3,d=digits(n^n);if(vecmin(d),print1(n,", "))) \\ Derek Orr, Aug 05 2014

A336480 a(n) is the smallest positive k such that Fibonorial(n) + k is a prime.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 37, 23, 47, 37, 29, 19, 47, 59, 19, 37, 71, 59, 31, 1, 239, 101, 739, 409, 43, 1, 167, 251, 73, 71, 419, 1567, 107, 83, 223, 191, 227, 449, 97, 173, 103, 523, 79, 137, 223, 1163, 661, 103, 103, 541, 227, 2383, 433, 71, 1069, 643, 251
Offset: 1

Views

Author

Mohamed Sami Gattoufi, Jul 22 2020

Keywords

Examples

			For n=5, Fibonorial(5) + 1 = 30 + 1 = 31 is a prime.

Crossrefs

Cf. A003266, A053408 (locations of 1's), A336481.

Programs

  • Mathematica
    Table[(NextPrime[Fibonorial[n]]-Fibonorial[n]),{n,1,50}]
NextPrime[#]-#&/@Fibonorial[Range[60]] (* Harvey P. Dale, Dec 24 2023 *)
  • PARI
    f(n) = prod(i=1, n, fibonacci(i)); \\ A003266
a(n) = my(fn=f(n)); nextprime(fn+1) - fn; \\ Michel Marcus, Jul 23 2020
Showing 1-7 of 7 results.

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