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A269790
Primes p such that 2*p + 79 is a square.
1
73, 181, 2341, 4861, 6121, 9901, 12601, 18973, 20161, 26641, 47701, 51481, 59473, 61561, 68041, 79561, 81973, 84421, 94573, 110881, 157321, 185401, 192781, 207973, 231841, 244261, 248473, 270073, 292573, 335341, 365473, 440821, 446473, 452161, 475273
OFFSET
1,1
COMMENTS
Primes of the form 2*k^2 + 2*k - 39.
2*p + h is not verified if h is an odd prime that belongs to A055025 because (2*h-1)/2 is a multiple of 2.
EXAMPLE
a(1) = 73 because 2*73 + 79 = 225, which is a square.
MATHEMATICA
Select[Prime[Range[50000]], IntegerQ[Sqrt[2 # + 79]] &]
PROG
(Magma) [p: p in PrimesUpTo(600000) | IsSquare(2*p+79)];
(PARI) lista(nn) = {forprime(p=2, nn, if(issquare(2*p + 79), print1(p, ", "))); } \\ Altug Alkan, Mar 24 2016
(Python)
from sympy import isprime
from gmpy2 import is_square
for p in range(0, 1000000):
if(is_square(2*p+79) and isprime(p)):print(p)
# Soumil Mandal, Apr 03 2016
CROSSREFS
Cf. A000040.
Subsequence of A002144, A045433, A061237, A068228.
Cf. similar sequences listed in A269784.
Sequence in context: A044786 A244774 A142550 * A142741 A088199 A140010
KEYWORD
nonn
AUTHOR
Vincenzo Librandi, Mar 24 2016
STATUS
approved