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.

A182785 Primes p such that 2*p^4-1 is also prime.

Original entry on oeis.org

2, 5, 7, 47, 79, 103, 131, 139, 149, 173, 197, 229, 307, 313, 331, 373, 439, 541, 547, 593, 659, 743, 761, 797, 853, 859, 863, 883, 919, 937, 1051, 1093, 1097, 1163, 1171, 1301, 1303, 1451, 1471, 1549, 1601, 1657, 1721, 1861, 1973, 2039, 2081, 2087, 2099, 2129, 2161, 2239, 2269, 2393, 2417, 2437, 2473, 2521
Offset: 1

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Author

Vincenzo Librandi, Dec 02 2010

Keywords

Links

Crossrefs

Cf. A182783, A182784, A106483 (2p^2-1 prime), A177104 (2p^3-1 prime), A309855 (2p^5-1 prime).

Programs

  • Magma
    [p: p in PrimesUpTo(2600)| IsPrime(2*p^4 - 1)]; // Vincenzo Librandi, Apr 17 2013
  • Mathematica
    Select[Prime[Range[500]], PrimeQ[2 #^4 - 1]&] (* Vincenzo Librandi, Apr 17 2013 *)

Formula

A000040 INTERSECT A182783.

A229627 a(n) is the smallest prime q such that 2*q^k - 1 is prime for k = 1, 2, ..., n.

Original entry on oeis.org

2, 2, 3, 92581, 385939, 464938699, 24137752519, 1095265755949
Offset: 1

Views

Author

Farideh Firoozbakht, Sep 27 2013

Keywords

Comments

The prime number 2 in the definition is used because 2 is the only prime p such that p*q^k - 1 can be prime for more than one prime q.
a(9) > 3*10^13. - Tyler Busby, Jan 14 2023

Crossrefs

Cf. A005382, A106483, A177104, A182785, A309855, A229626.

Programs

  • Mathematica
    a[1]=2;a[n_]:=a[n]=(For[m=PrimePi[a[n-1]],Union[Table[PrimeQ[2 Prime[m]^k-1],{k,n}]]!={True},m++];Prime[m])
  • PARI
    a(n)=forprime(m=2,,for(k=1,n,if(!ispseudoprime(2*m^k-1), next(2))); return(m)) \\ Charles R Greathouse IV, Oct 01 2013

Extensions

a(7) from Giovanni Resta, Oct 01 2013
a(8) from Tyler Busby, Jan 06 2023

A309854 Numbers k such that 2*k^5 - 1 is prime.

Original entry on oeis.org

6, 7, 10, 12, 15, 22, 34, 46, 57, 60, 64, 75, 81, 82, 84, 94, 112, 117, 129, 132, 151, 160, 169, 171, 175, 186, 196, 210, 214, 222, 225, 255, 264, 292, 301, 309, 315, 330, 357, 364, 369, 370, 379, 381, 384, 400, 412, 417, 426, 430, 454, 474, 516, 547, 549, 582, 610, 631, 636, 655
Offset: 1

Views

Author

R. J. Mathar, Aug 20 2019

Keywords

Links

Crossrefs

Cf. A214289 (2*k^3 - 1 prime), A182783 (2*k^4 - 1 prime), A309855 (subset of primes).

Programs

  • Maple
    filter:= k -> isprime(2*k^5-1):
select(filter, [$1..1000]); # Robert Israel, Oct 29 2023
  • PARI
    isok(k) = isprime(2*k^5 - 1); \\ Michel Marcus, Jul 22 2021
Showing 1-3 of 3 results.

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

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