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.

A163077 Numbers k such that k$ + 1 is prime. Here '$' denotes the swinging factorial function (A056040).

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 8, 9, 14, 15, 24, 27, 31, 38, 44, 45, 49, 67, 76, 92, 99, 119, 124, 133, 136, 139, 144, 168, 171, 185, 265, 291, 332, 368, 428, 501, 631, 680, 689, 696, 765, 789, 890, 1034, 1233, 1384, 1517, 1615, 1634, 1809, 2632, 2762, 3925, 4419, 5108, 5426
Offset: 1

Views

Author

Peter Luschny, Jul 21 2009

Keywords

Examples

			0$ + 1 = 1 + 1 = 2 is prime, so 0 is in the sequence.

Links

Crossrefs

Cf. A002981, A163078, 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[0, 8660], fQ] (* Robert G. Wilson v, Aug 09 2010 *)
  • PARI
    is(k) = ispseudoprime(1+k!/(k\2)!^2); \\ Jinyuan Wang, Mar 22 2020

Extensions

a(45)-a(56) from Robert G. Wilson v, Aug 09 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

A163080 Primes p such that p$ - 1 is also prime. Here '$' denotes the swinging factorial function (A056040).

Original entry on oeis.org

3, 5, 7, 13, 41, 47, 83, 137, 151, 229, 317, 389, 1063, 2371, 6101, 7873, 13007, 19603
Offset: 1

Views

Author

Peter Luschny, Jul 21 2009

Keywords

Comments

a(n) are the primes in A163078.

Examples

			3 is prime and 3$ - 1 = 5 is prime, so 3 is in the sequence.

Links

Crossrefs

Cf. A056040, A103317, A163079, A163078.

Programs

  • Maple
    a := proc(n) select(isprime,select(k -> isprime(A056040(k)-1),[$0..n])) end:
  • Mathematica
    sf[n_] := n!/Quotient[n, 2]!^2; Select[Prime /@ Range[200], PrimeQ[sf[#] - 1] &] (* Jean-François Alcover, Jun 28 2013 *)
  • PARI
    is(k) = isprime(k) && ispseudoprime(k!/(k\2)!^2-1); \\ Jinyuan Wang, Mar 22 2020

Extensions

a(14)-a(18) 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.

Links

Crossrefs

Cf. A056040, A103319, A163074-A163083.

Programs

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

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