A106484 -id:A106484 - 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

A106482 Number of prime factors (with multiplicity) of A007588(n).

Original entry on oeis.org

0, 0, 2, 2, 3, 3, 3, 2, 4, 4, 3, 2, 5, 2, 4, 3, 6, 2, 4, 3, 5, 3, 3, 3, 5, 3, 4, 5, 4, 3, 5, 3, 7, 4, 3, 4, 5, 4, 3, 3, 6, 2, 4, 2, 6, 4, 3, 3, 7, 3, 4, 4, 4, 3, 8, 4, 5, 4, 5, 2, 6, 3, 3, 4, 7, 5, 5, 3, 5, 3, 5, 3, 7, 2, 4, 5, 4, 4, 6, 3, 6, 5, 5, 3, 6, 3, 4, 3, 6, 4, 6, 3, 4, 5, 4, 3, 8, 3, 4, 5, 6

Offset: 0

Jonathan Vos Post, May 03 2005

			73*(2*73^2 - 1) = 777961 = 73 * 10657, which has two prime factors, so a(73) = 2.
100*(2*100^2 - 1) = 1999900 = 2^2 * 5^2 * 7 * 2857 has 6 prime factors.

Cf. A001222, A007588, A106483, A106484.

a:= n-> numtheory[bigomega](n*(2*n^2-1)):
seq(a(n), n=0..100);  # Alois P. Heinz, Mar 03 2023

a(n) = A001222(A007588(n)).

a(78) corrected by Sean A. Irvine, Mar 03 2023

cp's OEIS Frontend

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

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