A182785 -id:A182785 - cp's OEIS frontend

A106483 Primes p such that 2*p^2 - 1 is also prime.

2, 3, 7, 11, 13, 17, 41, 43, 59, 73, 109, 113, 127, 137, 157, 179, 181, 197, 199, 211, 251, 263, 277, 293, 311, 353, 367, 379, 409, 419, 433, 487, 563, 571, 577, 617, 619, 659, 701, 739, 743, 757, 797, 811, 827, 829, 839, 857, 937, 941, 1009, 1039, 1063

Offset: 1

Jonathan Vos Post, May 03 2005

Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)

Cf. A000040, A001358, A007588, A106482, A106484, A177104 (2p^3-1 prime), A182785 (2p^4-1 prime)

Cf. A092057 (2p^2 - 1).

[p: p in PrimesUpTo(2500)|  IsPrime(2*p^2-1)]; // Vincenzo Librandi, Jan 29 2011

q:= p-> andmap(isprime, [p, 2*p^2-1]):
select(q, [$2..2000])[];  # Alois P. Heinz, Jun 21 2022

Select[Table[Prime[n], {n, 500}], PrimeQ[2*#^2 - 1] &] (* Ray Chandler, May 03 2005 *)

a(n) is in this sequence iff A007588(a(n)) is an element of A001358.
a(n) is in this sequence iff A106482(a(n)) = 2.
a(n) is in this sequence iff a(n) is prime and 2*a(n)^2-1 is also prime.
a(n) = prime(A092058(n)). - R. J. Mathar, Aug 20 2019

Extended by Ray Chandler, May 03 2005

A182783 Numbers k such that 2*k^4 - 1 is a prime.

Original entry on oeis.org

2, 5, 6, 7, 8, 9, 14, 16, 21, 27, 28, 34, 42, 44, 47, 48, 50, 51, 62, 63, 65, 68, 70, 75, 76, 79, 82, 84, 93, 96, 98, 103, 106, 114, 120, 121, 124, 131, 133, 138, 139, 147, 148, 149, 156, 166, 169, 173, 174, 182, 195, 197, 201, 203, 216, 218, 225, 229, 237, 240, 243, 247, 253, 275, 282, 292, 299, 300, 307, 309, 310

Offset: 1

Vincenzo Librandi, Dec 02 2010

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

Cf. A182784, A182785.

Magma
```
[n: n in [1..1000]| IsPrime(2*n^4-1)];
```

Select[Range[350],PrimeQ[2#^4-1]&] (* Harvey P. Dale, Sep 12 2011 *)

A309855 Primes p such that 2*p^5-1 is also prime.

Original entry on oeis.org

7, 151, 379, 547, 631, 727, 769, 1531, 1627, 1741, 1789, 1999, 2131, 2437, 2659, 2797, 2857, 2917, 3217, 3331, 3511, 3919, 3931, 4591, 4651, 4759, 4801, 4831, 4957, 5281, 5689, 5701, 5779, 5821, 5881, 6067, 6217, 6361, 6619, 6871, 7039, 7309, 7489, 7927, 8179, 8221, 8329, 8581, 8641

Offset: 1

R. J. Mathar, Aug 20 2019

nonn

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A182785 (2*p^4-1 prime), A177104 (2*p^3-1 prime), A309854 (2*n^5-1 prime).

Select[Range[10000], PrimeQ[#]&&PrimeQ[2*(#^5)-1] &] (* Metin Sariyar, Aug 21 2019 *)
Select[Prime[Range[1100]],PrimeQ[2#^5-1]&] (* Harvey P. Dale, Jul 19 2025 *)

A000040 INTERSECT A309854.

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

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

Farideh Firoozbakht, Sep 27 2013

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

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

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])

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

a(7) from Giovanni Resta, Oct 01 2013

a(8) from Tyler Busby, Jan 06 2023

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A106483 Primes p such that 2*p^2 - 1 is also prime.

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A182783 Numbers k such that 2*k^4 - 1 is a prime.

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A309855 Primes p such that 2*p^5-1 is also prime.

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

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

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