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A289135
Prime numbers p such that 3*p - 2 is the square of a prime number.
2
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
KEYWORD
nonn
AUTHOR
Dimitris Valianatos, Jun 25 2017
STATUS
approved