A247101 Primes p such that 2*(p^2-1) - 1 and 2*(p^2-1) + 1 are also primes.

2, 11, 41, 59, 181, 379, 571, 659, 1429, 1439, 1721, 1879, 2029, 2239, 2351, 2381, 2579, 2671, 3209, 3581, 4159, 4229, 4271, 4969, 4999, 6299, 6451, 6551, 7349, 7841, 10391, 10399, 11059, 11551, 12841, 13049, 13159, 13619, 14071, 15329, 15581, 15889, 16811, 17231, 17749, 18719, 20219

Offset

1,1

Comments

Subsequence of prime terms of A249446.

Links

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

Example

2 is in this sequence because 2, 2*(2^2-1) - 1 = 5 and 2*(2^2-1) + 1 = 7 are all primes.

Mathematica

Select[Range[25000], PrimeQ[#] && PrimeQ[2 #^2 - 3] && PrimeQ[2 #^2 - 1] &] (* Vincenzo Librandi, Nov 19 2014 *)
Select[Prime[Range[2500]], AllTrue[2(#^2-1)+{1, -1}, PrimeQ]&] (* Harvey P. Dale, Nov 27 2025 *)

Prog

(Magma) [ n: n in [1..22000] | IsPrime(n) and IsPrime(2*(n^2-1)-1) and IsPrime(2*(n^2-1)+1) ];

Crossrefs

Cf. A249446.

Sequence in context: A377380 A154813 A168367 * A386092 A080093 A175447

Adjacent sequences: A247098 A247099 A247100 * A247102 A247103 A247104

Keyword

nonn

Author

Juri-Stepan Gerasimov, Nov 18 2014

Status

approved