A182783 -id:A182783 - cp's OEIS frontend

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

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

Vincenzo Librandi, Dec 02 2010

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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

[p: p in PrimesUpTo(2600)| IsPrime(2*p^4 - 1)]; // Vincenzo Librandi, Apr 17 2013

Select[Prime[Range[500]], PrimeQ[2 #^4 - 1]&] (* Vincenzo Librandi, Apr 17 2013 *)

A000040 INTERSECT A182783.

A182784 Primes of the form 2*n^4-1.

Original entry on oeis.org

31, 1249, 2591, 4801, 8191, 13121, 76831, 131071, 388961, 1062881, 1229311, 2672671, 6223391, 7496191, 9759361, 10616831, 12499999, 13530401, 29552671, 31505921, 35701249, 42762751, 48019999, 63281249, 66724351, 77900161, 90424351, 99574271, 149610401

Offset: 1

Vincenzo Librandi, Dec 02 2010

Subsequence of A066436. - R. J. Mathar, Dec 02 2010

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A182783, A182785.

[a: n in [1..350] | IsPrime(a) where a is 2*n^4-1];

Select[Table[2 n^4 - 1, {n, 100}], PrimeQ] (* Vincenzo Librandi, Sep 01 2012 *)

a(n) = 2*A182783(n)^4-1. - R. J. Mathar, Dec 02 2010

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

R. J. Mathar, Aug 20 2019

nonn

Robert Israel, Table of n, a(n) for n = 1..10000

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

filter:= k -> isprime(2*k^5-1):
select(filter, [$1..1000]); # Robert Israel, Oct 29 2023

isok(k) = isprime(2*k^5 - 1); \\ Michel Marcus, Jul 22 2021

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

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A182784 Primes of the form 2*n^4-1.

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Magma

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

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