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.

A163075 Primes of the form k$ + 1. Here '$' denotes the swinging factorial function (A056040).

Original entry on oeis.org

2, 3, 7, 31, 71, 631, 3433, 51481, 2704157, 280816201, 4808643121, 35345263801, 2104098963721, 94684453367401, 1580132580471901, 483701705079089804581, 6892620648693261354601, 410795449442059149332177041, 2522283613639104833370312431401
Offset: 1

Views

Author

Peter Luschny, Jul 21 2009

Keywords

Examples

			Since 3$ = 4$ = 6 the prime 7 is listed, however only once.
		

Crossrefs

Cf. A056040, A088332, A163077 (arguments k), A163074, A163076.

Programs

  • Maple
    a := proc(n) select(isprime, map(x -> A056040(x)+1,[$1..n])) end:
  • Mathematica
    Reap[Do[f = n!/Quotient[n, 2]!^2; If[PrimeQ[p = f + 1], Sow[p]], {n, 1, 70}]][[2, 1]] // Union (* Jean-François Alcover, Jun 28 2013 *)

Extensions

More terms from Jinyuan Wang, Mar 22 2020

A163076 Primes of the form k$ - 1. Here '$' denotes the swinging factorial function (A056040).

Original entry on oeis.org

5, 19, 29, 139, 251, 12011, 48619, 51479, 155117519, 81676217699, 1378465288199, 5651707681619, 386971244197199, 1580132580471899, 30067266499541039, 6637553085023755473070799, 35257120210449712895193719, 399608854866744452032002440111
Offset: 1

Views

Author

Peter Luschny, Jul 21 2009

Keywords

Examples

			Since 4$ = 6 the prime 5 is listed.
		

Crossrefs

Cf. A055490, A056040, A163078 (arguments k), A163074, A163075.

Programs

  • Maple
    a := proc(n) select(isprime, map(x -> A056040(x)-1,[$1..n])); sort(%) end:
  • Mathematica
    Reap[Do[f = n!/Quotient[n, 2]!^2; If[PrimeQ[p = f - 1], Sow[p]], {n, 1, 70}]][[2, 1]] // Union (* Jean-François Alcover, Jun 28 2013 *)

Extensions

More terms from Jinyuan Wang, Mar 22 2020

A163081 Primes of the form p$ + 1 where p is prime, where '$' denotes the swinging factorial (A056040).

Original entry on oeis.org

3, 7, 31, 4808643121, 483701705079089804581, 3283733939424401442167506310317720418331001
Offset: 1

Views

Author

Peter Luschny, Jul 21 2009

Keywords

Comments

The values of p are 2, 3, 5, 31, 67, 139 which is A163079. Subsequence of A163075 (primes of the form k$ + 1).

Examples

			3 and 3$ + 1 = 7 are prime, so 7 is a member.
		

Crossrefs

Programs

  • Maple
    a := proc(n) select(isprime,[$2..n]); select(isprime, map(x -> A056040(x)+1,%)) end:

A163082 Primes of the form p$ - 1 where p is prime, where '$' denotes the swinging factorial (A056040).

Original entry on oeis.org

5, 29, 139, 12011, 5651707681619, 386971244197199, 35257120210449712895193719, 815027488562171580969632861193966578650499
Offset: 1

Views

Author

Peter Luschny, Jul 21 2009

Keywords

Comments

The first values of p are 3, 5, 7, 13, 41 from A163080. Subsequence of A163076 (primes of the form k$ - 1).

Examples

			3 and 3$ - 1 = 5 are prime, so 5 is a member.
		

Crossrefs

Programs

  • Maple
    a := proc(n) select(isprime,[$2..n]); select(isprime, map(x -> A056040(x)-1,%)) end:
Showing 1-4 of 4 results.