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.

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

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.

Links

Crossrefs

Cf. A056040, A163074-A163083.

Programs

  • Maple
    a := proc(n) select(isprime,[$2..n]); select(isprime, map(x -> A056040(x)-1,%)) end:
Showing 1-3 of 3 results.

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

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