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 1-3 of 3 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.

Links

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

A163079 Primes p such that p$ + 1 is also prime. Here '$' denotes the swinging factorial function (A056040).

Original entry on oeis.org

2, 3, 5, 31, 67, 139, 631, 9743, 16253, 17977, 27901, 37589
Offset: 1

Views

Author

Peter Luschny, Jul 21 2009

Keywords

Comments

a(n) are the primes in A163077.

Examples

			5 is prime and 5$ + 1 = 30 + 1 = 31 is prime, so 5 is in the sequence.

Links

Crossrefs

Cf. A002981, A062363, A093804, A163077.
Cf. A056040. - Robert G. Wilson v, Aug 09 2010

Programs

  • Maple
    a := proc(n) select(isprime,select(k -> isprime(A056040(k)+1),[$0..n])) end:
  • Mathematica
    f[n_] := 2^(n - Mod[n, 2])*Product[k^((-1)^(k + 1)), {k, n}]; p = 2; lst = {}; While[p < 38000, a = f@p + 1; If[ PrimeQ@a, AppendTo[ lst, p]; Print@p]; p = NextPrime@p]; lst (* Robert G. Wilson v, Aug 08 2010 *)
  • PARI
    is(k) = isprime(k) && ispseudoprime(1+k!/(k\2)!^2); \\ Jinyuan Wang, Mar 22 2020

Extensions

a(8)-a(12) from Robert G. Wilson v, Aug 08 2010

A163078 Numbers k such that k$ - 1 is prime. Here '$' denotes the swinging factorial function (A056040).

Original entry on oeis.org

3, 4, 5, 6, 7, 10, 13, 15, 18, 30, 35, 39, 41, 47, 49, 58, 83, 86, 102, 111, 137, 151, 195, 205, 226, 229, 317, 319, 321, 368, 389, 426, 444, 477, 534, 558, 567, 738, 804, 882, 1063, 1173, 1199, 1206, 1315, 1624, 1678, 1804, 2371, 2507, 2541, 2844, 3084, 3291
Offset: 1

Views

Author

Peter Luschny, Jul 21 2009

Keywords

Examples

			4$ - 1 = 6 - 1 = 5 is prime, so 4 is in the sequence.

Links

Crossrefs

Cf. A002982, A056040, A163077, A163079, A163080.

Programs

  • Maple
    a := proc(n) select(x -> isprime(A056040(x)-1),[$0..n]) end:
  • Mathematica
    fQ[n_] := PrimeQ[ -1 + 2^(n - Mod[n, 2])*Product[k^((-1)^(k + 1)), {k, n}]]; Select[ Range@ 3647, fQ] (* Robert G. Wilson v, Aug 09 2010 *)
  • PARI
    is(k) = ispseudoprime(k!/(k\2)!^2-1); \\ Jinyuan Wang, Mar 22 2020

Extensions

a(42)-a(54) from Robert G. Wilson v, Aug 09 2010
Showing 1-3 of 3 results.

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

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