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 1-5 of 5 results.

A073828 Primes of the form 1 + 0!*1!*2!*...*n! (subsequence of A019515).

Original entry on oeis.org

2, 2, 3, 13, 125411328001, 69113789582492712943486800506462734562847413501952000000000000001
Offset: 1

Views

Author

Rick L. Shepherd, Aug 16 2002

Keywords

Comments

a(4) = 125411328001 and the 65-digit a(5) have been certified prime with Primo. Any additional terms are too big to include here. a(3) = 13 and a(4) have twin primes, 11 and 125411327999 (also certified prime with Primo). No other primes of the form 0!*1!*2!*...*n! - 1 exist for n < 108.

Examples

			a(0) = 1 + 0! (0=A073827(0)) = 1 + 1 = 2. a(1) = 1 + 0!*1! (1=A073827(1)) = 1 + 1*1 = 2. a(4) = 1 + 0!*1!*2!*3!*4!*5!*6!*7! (7=A073827(4)) = 1 + 1*1*2*6*24*120*720*5040 = 125411328001

References

  • Ryser, H. J. Combinatorial Mathematics. Buffalo, NY: Math. Assoc. Amer., p. 53, 1963.

Links

Crossrefs

Cf. A073827 (corresponding n), A000178 (superfactorials), A019515 (supersequence: superfactorials + 1), A000142 (factorials).

Programs

  • PARI
    pr=1; for(n=0,115, pr=pr*n!; if(isprime(pr+1), print1(pr+1,",")))

Formula

a(k) = 1 + 0!*1!*2!*...*A073827(k)!.

A030522 Product of first n palindromic primes minus 1.

Original entry on oeis.org

1, 5, 29, 209, 2309, 233309, 30563609, 4615105109, 835334024909, 159548798757809, 49938774011194529, 17628387225951669089, 6575388435279972570569, 2518373770712229494528309
Offset: 1

Views

Author

Felice Russo

Keywords

Comments

The subsequence which are themselves primes begins: 5, 29, 2309, 4615105109, 2518373770712229494528309. - Jonathan Vos Post, Feb 09 2011

Links

Crossrefs

Cf. A019515, A030521.

Programs

  • Mathematica
    palQ[n_]:=Module[{idn=IntegerDigits[n]},idn==Reverse[idn]]; #-1&/@Rest[ FoldList[ Times,1,Select[Prime[Range[200]],palQ]]] (* Harvey P. Dale, Jun 21 2011 *)
FoldList[Times,Select[Prime[Range[100]],PalindromeQ]]-1 (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Dec 29 2018 *)

Extensions

Corrected and extended by Larry Reeves (larryr(AT)acm.org), Sep 25 2000
Corrected by D. S. McNeil, Aug 20 2010

A030521 Product of first n palindromic primes plus 1.

Original entry on oeis.org

3, 7, 31, 211, 2311, 233311, 30563611, 4615105111, 835334024911, 159548798757811, 49938774011194531, 17628387225951669091, 6575388435279972570571, 2518373770712229494528311, 1830857731307790842522081371, 1385959302599997667789215597091
Offset: 1

Views

Author

Felice Russo

Keywords

Comments

The subsequence of those values which are themselves primes begins: 3, 7, 31, 211, 2311, 6575388435279972570571. - Jonathan Vos Post, Feb 09 2011

Crossrefs

Cf. A019515, A030522.

Programs

  • Mathematica
    palpQ[n_]:=Module[{idn=IntegerDigits[n]},idn==Reverse[idn]]; #+1&/@FoldList[ Times, 1,Select[Prime[Range[500]],palpQ]]  (* Harvey P. Dale, Apr 23 2011 *)

Extensions

Corrected and extended by Patrick De Geest, Sep 15 2000
More terms from Harvey P. Dale, Apr 23 2011

A073827 Numbers n such that 1 + 0!*1!*2!*...*n! is prime.

Original entry on oeis.org

0, 1, 2, 3, 7, 14
Offset: 1

Views

Author

Rick L. Shepherd, Aug 16 2002

Keywords

Comments

Any additional terms are greater than 115 with the next prime having 9744 or more digits.

Crossrefs

Cf. A073828 (corresponding primes), A000178 (superfactorials), A019515.

Programs

  • PARI
    pr=1; for(n=0,115, pr=pr*n!; if(isprime(pr+1), print1(n,",")))

A030428 a(n) = 0! * 1! * 2! * ... * n! - 1.

Original entry on oeis.org

0, 0, 1, 11, 287, 34559, 24883199, 125411327999, 5056584744959999, 1834933472251084799999, 6658606584104736522239999999, 265790267296391946810949631999999999, 127313963299399416749559771247411199999999999
Offset: 0

Views

Author

Felice Russo

Keywords

Crossrefs

Cf. A019515, A000178.

Programs

  • Mathematica
    Table[BarnesG[n] - 1, {n, 2, 12}] (* Zerinvary Lajos, Jul 16 2009 *)
FoldList[Times,1,Range[10]!]-1 (* Harvey P. Dale, Feb 05 2012 *)

Formula

a(n) = A000178(n) - 1. - Sean A. Irvine, Mar 31 2020

Extensions

Name corrected by Arkadiusz Wesolowski, Oct 03 2011
More terms from Harvey P. Dale, Feb 05 2012
Showing 1-5 of 5 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.