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 1-6 of 6 results.

A076133 Numbers k such that 2*k! - 1 is prime.

Original entry on oeis.org

2, 3, 4, 5, 6, 7, 14, 15, 17, 22, 28, 91, 253, 257, 298, 659, 832, 866, 1849, 2495, 2716, 2773, 2831, 3364, 5264, 7429, 28539, 32123, 37868, 65591, 113920
Offset: 1

Views

Author

Phillip L. Poplin (plpoplin(AT)bellsouth.net), Oct 30 2002

Keywords

Comments

a(32) > 116000. - Serge Batalov, Jun 06 2025

Examples

			k = 5 is here because 2*5! - 1 = 239 is prime.

Crossrefs

Cf. A051915.
Cf. A002982, A076134, A099350, A099351, A180627, A180628, A180629, A180630, A180631.

Programs

  • Magma
    [n: n in [1..600] | IsPrime(2*Factorial(n)-1)]; // Vincenzo Librandi, Feb 20 2015
  • Mathematica
    Select[Range[8000], PrimeQ[2 #! - 1] &] (* Vincenzo Librandi, Feb 20 2015 *)
  • PARI
    is(k) = ispseudoprime(2*k!-1); \\ Jinyuan Wang, Feb 04 2020

Extensions

a(24)-a(29) from Serge Batalov, Feb 18 2015
a(30) from Serge Batalov, Jun 03 2025
a(31) from Serge Batalov, Jun 06 2025

A076134 Numbers k such that 3*k! - 1 is prime.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 9, 12, 17, 26, 76, 379, 438, 1695, 6709, 13313, 18504, 19021, 24488, 45552, 49085, 65451
Offset: 1

Views

Author

Phillip L. Poplin (plpoplin(AT)bellsouth.net), Oct 30 2002

Keywords

Comments

a(23) > 80000. - Serge Batalov, Jun 09 2025

Examples

			k = 5 is here because 3*5! - 1 = 359 is prime.

Crossrefs

Cf. A051915, A076134.
Cf. A002982, A076133, A099350, A099351, A180627, A180628, A180629, A180630, A180631.

Programs

  • Maple
    for n from 0 to 1000 do if isprime(3*n! - 1) then print(n) end if end do;
  • Mathematica
    Select[Range[0, 10^3], PrimeQ[3 #! - 1] &] (* Robert Price, May 27 2019 *)
  • PARI
    isok(n) = isprime(3*n! - 1); \\ Michel Marcus, Nov 13 2016
  • PFGW
    ABC2 3*$a!+1
a: from 1 to 1000 // Jinyuan Wang, Feb 04 2020

Extensions

a(15)-a(21) from Roger Karpin, Nov 13 2016
a(22) from Serge Batalov, Jun 08 2025

A099350 Numbers k such that 4*k! - 1 is prime.

Original entry on oeis.org

0, 1, 2, 3, 5, 6, 10, 11, 51, 63, 197, 313, 579, 1264, 2276, 2669, 4316, 4382, 4678, 7907, 10843
Offset: 1

Views

Author

Brian Kell, Oct 12 2004

Keywords

Comments

a(19) > 4570. - Jinyuan Wang, Feb 04 2020

Examples

			k = 5 is here because 4*5! - 1 = 479 is prime.

Crossrefs

Cf. A076680.
Cf. A002982, A076133, A076134, A099351, A180627, A180628, A180629, A180630, A180631.

Programs

  • Maple
    for n from 0 to 1000 do if isprime(4*n! - 1) then print(n) end if end do;
  • Mathematica
    For[n = 0, True, n++, If[PrimeQ[4 n! - 1], Print[n]]] (* Jean-François Alcover, Sep 23 2015 *)
  • PARI
    is_A099350(n)=ispseudoprime(n!*4-1) \\ M. F. Hasler, Sep 20 2015

Extensions

a(14) from Alois P. Heinz, Sep 21 2015
a(15)-a(16) from Jean-François Alcover, Sep 23 2015
a(17)-a(18) from Jinyuan Wang, Feb 04 2020
a(19) from Michael S. Branicky, May 16 2023
a(20)-a(21) from Michael S. Branicky, Jul 11 2024

A099351 Numbers k such that 5*k! - 1 is prime.

Original entry on oeis.org

3, 5, 8, 13, 20, 25, 51, 97, 101, 241, 266, 521, 1279, 1750, 2204, 2473, 4193, 5181, 10080
Offset: 1

Views

Author

Brian Kell, Oct 12 2004

Keywords

Comments

a(15) > 1879. - Jinyuan Wang, Feb 04 2020
a(17) > 3500. - Michael S. Branicky, Mar 06 2021

Examples

			k = 5 is here because 5*5! - 1 = 599 is prime.

Links

Crossrefs

Cf. A002982, A076133, A076134, A099350, A180627, A180628, A180629, A180630, A180631.

Programs

  • Maple
    for n from 0 to 1000 do if isprime(5*n! - 1) then print(n) end if end do;
  • Mathematica
    Select[Range[550],PrimeQ[5#!-1]&] (* Harvey P. Dale, Nov 27 2013 *)
  • PARI
    is(n)=ispseudoprime(5*n!-1) \\ Charles R Greathouse IV, Jun 13 2017
  • Python
    from sympy import isprime
from math import factorial
print([k for k in range(300) if isprime(5*factorial(k) - 1)]) # Michael S. Branicky, Mar 05 2021

Extensions

a(13)-a(14) from Jinyuan Wang, Feb 04 2020
a(15)-a(16) from Michael S. Branicky, Mar 05 2021
a(17)-a(18) from Michael S. Branicky, Apr 03 2023
a(19) from Michael S. Branicky, Jul 12 2024

A180628 Numbers k such that 7*k! - 1 is prime.

Original entry on oeis.org

2, 3, 4, 5, 6, 7, 8, 12, 23, 25, 31, 57, 74, 86, 140, 240, 310, 703, 713, 796, 1028, 1102, 1924, 3469, 3990
Offset: 1

Views

Author

Robert G. Wilson v, Sep 13 2010

Keywords

Comments

a(26) > 12000. - Michael S. Branicky, Jul 07 2024

Links

Crossrefs

Cf. A002982, A076133, A076134, A099350, A099351, A180627, A180629, A180630, A180631.

Programs

  • Mathematica
    fQ[n_] := PrimeQ[7 n! - 1]; k = 0; lst = {}; While[k < 1501, If[ fQ@k, AppendTo[lst, k]; Print@k]; k++ ]; lst
Select[Range[4000],PrimeQ[7#!-1]&] (* Harvey P. Dale, Apr 22 2024 *)
  • PARI
    is(k) = ispseudoprime(7*k!-1); \\ Jinyuan Wang, Feb 03 2020

Extensions

a(23) from Jinyuan Wang, Feb 03 2020
a(24)-a(25) from Michael S. Branicky, Apr 25 2023

A180630 Numbers k such that 9*k! - 1 is prime.

Original entry on oeis.org

2, 3, 12, 15, 16, 25, 30, 38, 59, 82, 114, 168, 172, 175, 213, 229, 251, 302, 311, 554, 2538, 3050, 3363, 12316
Offset: 1

Views

Author

Robert G. Wilson v, Sep 13 2010

Keywords

Comments

a(22) > 2575. - Jinyuan Wang, Feb 03 2020

Links

Crossrefs

Cf. A002982, A076133, A076134, A099350, A099351, A180627, A180628, A180629, A180631.

Programs

  • Mathematica
    fQ[n_] := PrimeQ[9 n! - 1]; k = 0; lst = {}; While[k < 1501, If[ fQ@k, AppendTo[lst, k]; Print@k]; k++ ]; lst
  • PARI
    is(k) = ispseudoprime(9*k!-1); \\ Jinyuan Wang, Feb 03 2020

Extensions

a(21) from Jinyuan Wang, Feb 03 2020
a(22)-a(23) from Michael S. Branicky, Apr 25 2023
a(24) from Michael S. Branicky, Nov 02 2024
Showing 1-6 of 6 results.

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

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