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 1-4 of 4 results.

A217650 Numbers k such that 2*k!!! - 1 is prime.

Original entry on oeis.org

2, 3, 4, 5, 11, 23, 27, 29, 36, 40, 41, 71, 89, 119, 127, 157, 163, 187, 652, 1374, 1518, 2922, 5193, 6663, 7455, 9739, 11569, 14103
Offset: 1

Views

Author

Michel Lagneau, Oct 09 2012

Keywords

Comments

k!!! is a triple factorial, see the definition in A007661.

Examples

			5 is in the sequence because 2*5!!! - 1 = 2*10 - 1 = 19 is prime.

Crossrefs

Cf. A007661, A217647, A217650.

Programs

  • Maple
    A:= n -> mul(k, k = select(k -> k mod 3 = n mod 3, [$1 .. n])): for p from 0 to 200 do:if type(2*A(p)-1,prime)=true then printf(`%d, `,p):else fi:od:
  • Mathematica
    lst={}; multiFactorial[n_, k_] := If[n < 1, 1, If[n < k + 1, n, n*multiFactorial[n - k, k]]]; Do[If[PrimeQ[2*multiFactorial[n, 3] - 1], AppendTo[lst, n]], {n, 0, 1000}]; lst
  • PARI
    is(n)=ispseudoprime(2*prod(i=0, (n-2)\3, n-3*i)-1) \\ Charles R Greathouse IV, Oct 09 2012
  • PFGW
    ABC2 2*$a!3-1
a: from 1 to 6000
Charles R Greathouse IV, Oct 09 2012

Extensions

a(20)-a(23) from Charles R Greathouse IV, Oct 09 2012
a(24)-a(25) from Jinyuan Wang, May 15 2021
a(26)-a(28) from Michael S. Branicky, Jul 25 2024

A217648 Primes of the form 2*k!!! + 1.

Original entry on oeis.org

3, 3, 5, 7, 37, 3889, 58321, 8377601, 22044961, 11154675863339008001, 4960821503667767721984001, 26284943176784413780354966093824000001, 9847302066569247971143106634078785893903902965760000001, 35900221830120178462218744565190401129929679752455520256000000001
Offset: 1

Views

Author

Michel Lagneau, Oct 09 2012

Keywords

Comments

k!!! is a triple factorial number (see the definition in A007661).
The corresponding k are in A217647.

Examples

			2*0!!! + 1 = 2*1 + 1 = 3 ;
2*1!!! + 1 = 2*1 + 1 = 3 ;
2*2!!! + 1 = 2*2 + 1 = 5 ;
2*3!!! + 1 = 2*3 + 1 = 7 ;
2*6!!! + 1 = 2*18 + 1 = 37.

Crossrefs

Cf. A007661, A217647.

Programs

  • Maple
    A:= n -> mul(k, k = select(k -> k mod 3 = n mod 3, [$1 .. n])): for p from 0 to 200 do:if type(2*A(p)+1,prime)=true then printf(`%d, `,2*A(p)+1):else fi:od:
  • Mathematica
    multiFactorial[n_, k_] := If[n < 1, 1, If[n < k + 1, n, n*multiFactorial[n - k, k]]]; Select[Table[2*multiFactorial[n, 3] + 1, {n, 0, 60}], PrimeQ]
Select[Table[2*Times@@Range[n,1,-3]+1,{n,0,150}],PrimeQ] (* Harvey P. Dale, Mar 30 2025 *)

A271392 Integers k such that 3*k!!! + 1 is prime where k!!! is A007661(k).

Original entry on oeis.org

2, 4, 5, 8, 9, 15, 16, 23, 27, 32, 34, 35, 38, 40, 46, 54, 57, 83, 87, 97, 162, 165, 223, 235, 282, 488, 503, 575, 673, 823, 857, 885, 965, 1112, 1401, 2288, 2569, 2788, 3133, 3539, 4070, 4654, 5020, 5613, 6720, 7773, 11256, 18023, 22196
Offset: 1

Views

Author

Altug Alkan, Apr 06 2016

Keywords

Comments

Corresponding primes are 7, 13, 31, 241, 487, 87481, 174721, 289027201, 21427701121, ...

Examples

			4 is a term because 3*4!!! + 1 = 13 is prime.

Crossrefs

Cf. A007661, A037083, A084438, A217647, A215779, A271396.

Programs

  • PARI
    is(k) = ispseudoprime(3*prod(i=0, (k-2)\3, k-3*i) + 1); \\ Jinyuan Wang, Jun 09 2021

Extensions

a(47) from Jinyuan Wang, Jun 09 2021
a(48)-a(49) from Michael S. Branicky, Aug 10 2024

A271396 Integers k such that 3*k!!! - 1 is prime where k!!! is A007661(k).

Original entry on oeis.org

0, 1, 2, 4, 5, 6, 7, 8, 10, 17, 25, 28, 31, 37, 38, 39, 46, 47, 49, 55, 67, 82, 85, 94, 98, 115, 120, 129, 167, 214, 216, 267, 293, 580, 732, 857, 993, 1012, 1069, 1308, 1430, 2366, 2974, 4017, 4870, 9034, 9061, 9752, 10657, 13847, 25390
Offset: 1

Views

Author

Altug Alkan, Apr 06 2016

Keywords

Comments

Corresponding primes are 2, 2, 5, 11, 29, 53, 83, 239, 839, 628319, 1825823999, 51123071999, ...

Examples

			4 is a term because 3*4!!! - 1 = 11 is prime.

Crossrefs

Cf. A007661, A037083, A084438, A217647, A215779, A271392.

Programs

  • Mathematica
    Select[Range[0,5000],PrimeQ[3Times@@Range[#,1,-3]-1]&] (* The program generates the first 45 terms of the sequence. *) (* Harvey P. Dale, Mar 29 2025 *)
  • PARI
    is(k) = ispseudoprime(3*prod(i=0, (k-2)\3, k-3*i) - 1); \\ Jinyuan Wang, Jun 09 2021

Extensions

a(46)-a(50) from Jinyuan Wang, Jun 09 2021
a(51) from Michael S. Branicky, Aug 09 2024
Showing 1-4 of 4 results.

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