A261810 n and (2*n^2 + 2*n - 1) are primes.

2, 3, 5, 11, 23, 59, 71, 113, 131, 137, 149, 179, 227, 257, 263, 269, 293, 317, 347, 353, 401, 419, 443, 449, 467, 557, 653, 659, 677, 683, 743, 773, 809, 839, 857, 881, 911, 929, 947, 977, 1019, 1049, 1277, 1301, 1319, 1433, 1571, 1697, 1847, 1871, 1901, 1913

Offset

1,1

Comments

Primes p such that (number of divisors of p * sum of divisors of p * product of divisors of p - 1) is also a prime.

Primes p such that (A000005(p) * A000203(p) * A007955(p) - 1) is also a prime.

See similar sequences of type primes p such that x is also a prime for some x wherein tau(p) = A000005(p) = number of divisors of p, sigma(p) = A000203(p) = sum of divisors of p and pod(p) = A007955(p) = product of divisors of p:

A001359 (for x = tau(p) + sigma(p) - 1) and x = tau(p) + pod(p)),

A005382 (for x = tau(p) * pod(p) - 1),

A005384 (for x = sigma(p) + pod(p), x = tau(p) * sigma(p) - 1 and x = tau(p) * pod(p) + 1),

A023200 (for x = tau(p) + sigma(p) + 1),

A023204 (for x = tau(p) + sigma(p) + pod(p) and x = tau(p) * sigma(p) + 1),

A053182 (for x = sigma(p) * pod(p) + 1),

A053184 (for x = sigma(p) * pod(p) - 1),

A158526 (for x = tau(p) * sigma(p) * pod(p) + 1).

For n >= 3, a(n) == 5 mod 6. - Robert Israel, Sep 02 2015

Links

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

Example

3 and 2*3^2 + 2*3 - 1 = 23 are primes.

Maple

select(t -> isprime(t) and isprime(2*t^2 + 2*t-1), [2, 3, seq(6*i-1, i=1..1000)]); # Robert Israel, Sep 02 2015

Mathematica

Select[Prime[Range[300]], PrimeQ[2 #^2 + 2 # - 1] &] (* Vincenzo Librandi, Sep 02 2015 *)

Prog

(Magma) [n: n in[1..10000] | IsPrime(n) and IsPrime(2*n*n + 2*n - 1)]
(PARI)  is(n)=isprime(n)&&isprime(2*n^2 + 2*n - 1) \\ Anders Hellström, Sep 01 2015

Crossrefs

Cf. A000005, A000203, A007955.

Cf. A001359, A005382, A005384, A023200, A023204, A053182, A053184, A158526.

Sequence in context: A027763 A233694 A338418 * A176499 A175234 A060696

Adjacent sequences: A261807 A261808 A261809 * A261811 A261812 A261813

Keyword

nonn

Author

Jaroslav Krizek, Sep 01 2015

Status

approved