A289135 Prime numbers p such that 3*p - 2 is the square of a prime number.

2, 17, 41, 97, 281, 457, 617, 937, 1777, 2081, 2297, 3137, 6257, 12161, 18097, 21001, 23057, 24121, 24481, 25577, 26321, 42961, 47881, 50441, 62497, 70841, 76481, 90481, 97561, 110977, 120401, 132721, 139537, 152777, 159161, 172321, 182041

Offset

1,1

Comments

Terms > 2 are congruent to either 1 or 17 mod 40. - Davide Rotondo, Feb 06 2024

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Formula

a(n) = (A109953(n)^2 + 2) / 3.

Mathematica

Select[Prime@ Range@ 20000, PrimeQ@ Sqrt[3 # - 2] &] (* Michael De Vlieger, Jun 26 2017 *)

Prog

(PARI) forprime(n=2, 10000, if(isprimepower(3*n-2)==2, print1(n", ")))
(PARI) list(lim)=my(v=List([2]), p); forprime(q=7, sqrtint(lim\1*3-2), if(isprime(p=(q^2+2)/3), listput(v, p))); Vec(v) \\ Charles R Greathouse IV, Jul 16 2017

Crossrefs

Cf. A109953.

Sequence in context: A000956 A031906 A045390 * A072582 A186687 A256145

Adjacent sequences: A289132 A289133 A289134 * A289136 A289137 A289138

Keyword

nonn

Author

Dimitris Valianatos, Jun 25 2017

Status

approved