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

Author

Dimitris Valianatos, Jun 25 2017

Keywords

• nonn

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

Crossrefs

Cf. A109953.

Programs

Mathematica

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

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

Formula

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