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.

A092075 Duplicate of A091415.

Original entry on oeis.org

2, 3, 4, 8, 13, 32, 41, 45, 59, 97, 107, 364, 421, 444, 1164
Offset: 1

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Author

Keywords

A007749 Numbers k such that k!! - 1 is prime.

Original entry on oeis.org

3, 4, 6, 8, 16, 26, 64, 82, 90, 118, 194, 214, 728, 842, 888, 2328, 3326, 6404, 8670, 9682, 27056, 44318, 76190, 100654, 145706
Offset: 1

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Author

N. J. A. Sloane

Keywords

Comments

a(n) is even for n>1. a(n) = 2*A091415(n-1) for n>1, where A091415(n) = {2, 3, 4, 8, 13, 32, 41, 45, 59, 97, 107, 364, 421, 444, 1164, 1738, 3202, 4335, 4841, ...} (numbers k such that k!*2^k - 1 is prime). Corresponding primes of the form k!!-1 are listed in A117141 = {2, 7, 47, 383, 10321919, 51011754393599, ...}. - Alexander Adamchuk, Nov 19 2006
The PFGW program has been used to certify all the terms up to a(25), using a deterministic test which exploits the factorization of a(n) + 1. - Giovanni Resta, Apr 22 2016

References

  • The Top Ten (a Catalogue of Primal Configurations) from the unpublished collections of R. Ondrejka, assisted by C. Caldwell and H. Dubner, March 11, 2000, Page 61.

Links

Crossrefs

Cf. A006882.
Cf. A091415 (n such that n!*2^n - 1 is prime), A117141 (primes of the form n!! - 1).

Programs

  • Maple
    select(t -> isprime(doublefactorial(t)-1), [3, seq(n,n=4..3000,2)]); # Robert Israel, Apr 21 2016
  • Mathematica
    a(1) = 3, for n>1 k=2;f=2;Do[k=k+2;f=f*k;If[PrimeQ[f-1],Print[k]],{n,2,5000}] (* Alexander Adamchuk, Nov 19 2006 *)
Select[Range[45000],PrimeQ[#!!-1]&] (* Harvey P. Dale, Aug 07 2013 *)
  • PARI
    print1(3);for(n=2, 1e3, if(ispseudoprime(n!<Charles R Greathouse IV, Jun 16 2011

Formula

a(n) = 2*A091415(n-1) for n>1. - Alexander Adamchuk, Nov 19 2006

Extensions

Entry updated by Robert G. Wilson v, Aug 18 2000
Corrected and extended by Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 03 2008
a(23)-a(24) from Sou Fukui, Jun 05 2015
a(25) from Sou Fukui, Apr 21 2016

A121859 Numbers n such that n!*3^n - 1 is prime.

Original entry on oeis.org

1, 2, 12, 20, 38, 45, 46, 105, 117, 143, 214, 1835, 2931, 7703, 11542, 19225
Offset: 1

Views

Author

Alexander Adamchuk, Sep 10 2006

Keywords

Comments

Corresponding primes of the form n!*3^n - 1 are a(n)!*3^a(n) - 1 ={2,17,254561089305599,8483004771271882804592639999,...}.
a(17) > 25000. - Robert Price, Jul 22 2013

Crossrefs

Cf. A091415, A002982.

Programs

  • Mathematica
    Do[f=n!*3^n-1;If[PrimeQ[f],Print[{n,f}]],{n,1,25000}]

Extensions

a(12)-a(16) from Robert Price, Jul 22 2013

A128882 a(n) = n!! - 1.

Original entry on oeis.org

0, 0, 1, 2, 7, 14, 47, 104, 383, 944, 3839, 10394, 46079, 135134, 645119, 2027024, 10321919, 34459424, 185794559, 654729074, 3715891199, 13749310574, 81749606399, 316234143224, 1961990553599, 7905853580624, 51011754393599
Offset: 0

Views

Author

Alexander Adamchuk, Apr 18 2007

Keywords

Comments

n divides a(n-1) and a(n+1) for n = {1, 2, 8, 11, 16, 19, 23, 31, 32, 43, 64, 67, 71, ...} which include all powers of 2 except 2^2 and some odd primes of the form 4k+3 belonging to A002145.
p^2 divides a(p-1) for odd prime p = 71.
p^2 divides a(p+1) for odd prime p = 23.
a(n) is prime for n = {3, 4, 6, 8, 16, 26, 64, 82, 90, 118, 194, 214, ...} = A007749; A007749(n) = 2*A091415(n-1) for n > 1. Corresponding primes of the form n!! - 1 are listed in A117141, cf. also A093173.

Links

Crossrefs

Cf. A006882, A002145, A117141, A093173, A007749, A091415.

Programs

  • Mathematica
    Table[ n!! - 1, {n,0,35} ]

Formula

a(n) = A006882(n) - 1.

A256594 Numbers k such that k!*2^k + 1 is prime.

Original entry on oeis.org

0, 1, 259, 16708, 18655, 26304, 61999, 110251
Offset: 1

Views

Author

Robert Price, Apr 03 2015

Keywords

Examples

			0 is in the sequence since 0!*2^0 + 1 = 2 is prime.

Crossrefs

Cf. A007749, A080778, A117141, A091415.

Programs

  • Magma
    [n: n in [0..3*10^2] | IsPrime(Factorial(n)*2^n+1)]; // Vincenzo Librandi, Apr 05 2015
  • Mathematica
    Select[Range[0, 20000], PrimeQ[2^#*#! + 1] &]
  • PARI
    for(n=0,300,if(ispseudoprime(n!*2^n+1),print1(n,", "))) \\ Derek Orr, Apr 05 2015
  • Python
    from sympy import factorial, isprime
for n in range(0,300):
    if isprime(factorial(n)*(2**n)+1):
        print(n, end=', ') # Stefano Spezia, Dec 06 2018

Formula

a(n) = A080778(n+1)/2 for n >= 2. - Amiram Eldar, Dec 06 2018

Extensions

a(6)-a(8), from the data at A080778, added by Amiram Eldar, Dec 06 2018

A236169 Numbers n such that n!*3^n + 1 is prime.

Original entry on oeis.org

0, 2, 3, 8, 13, 19, 124, 199, 288, 359, 692, 3610, 5316, 5372, 7442, 8251, 14288, 16883, 17131
Offset: 1

Views

Author

Robert Price, Jan 19 2014

Keywords

Comments

a(20) > 25000.
Corresponding primes are all verified prime (i.e., not probable prime): 2, 19, 163, 264539521, 9927882482918401, 141383412854531380076544001, ...

Crossrefs

Cf. A091415, A002982, A121859.

Programs

  • Mathematica
    Do[f=n!*3^n+1;If[PrimeQ[f],Print[{n,f}]],{n,0,25000}]
  • PARI
    isok(n) = isprime(n!*3^n + 1); \\ Michel Marcus, Jul 23 2017

Extensions

a(1)=0 prepended by Robert Price, Jul 22 2017

A122719 Primes p such that (2p)!! - 1 is prime.

Original entry on oeis.org

2, 3, 13, 41, 59, 97, 107, 421, 1663, 22159
Offset: 1

Views

Author

Alexander Adamchuk, Sep 23 2006

Keywords

Comments

a(n) are the primes from A091415[n] = {2,3,4,8,13,32,41,45,59,97,107,364,421,...} Numbers n such that n!*2^n - 1 is prime. Corresponding primes of the form (2p)!! - 1 are {3,5,270269,26226140915375977206881249, 58431212742946338570036120182498518593749,...}
No other terms up to 3000. - Stefan Steinerberger, Sep 09 2007

Crossrefs

Cf. A007749, A117141, A091415.

Programs

  • Mathematica
    Select[Prime[Range[651]],PrimeQ[(2#)!!-1]&]

Extensions

a(9) from Stefan Steinerberger, Sep 09 2007
a(10) from Robert Price, Nov 26 2013
Showing 1-7 of 7 results.

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

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