A269786 Primes p such that 2*p + 31 is a square.

97, 349, 997, 1609, 2797, 3769, 6829, 7549, 10789, 11689, 13597, 15649, 16729, 22669, 28069, 32497, 40597, 44089, 49597, 59497, 63709, 70297, 74869, 86929, 89449, 94597, 113749, 122497, 128509, 144169, 147409, 153997, 164149, 181789, 196549, 200329, 207997

Offset: 1

Author

Vincenzo Librandi, Mar 22 2016

Keywords

• nonn

Comments

Primes of the form 2*k^2 + 2*k - 15.

Crossrefs

Cf. A000040.

Subsequence of A061241, A142108.

Cf. similar sequences listed in A269784.

Programs

Magma

[p: p in PrimesUpTo(300000) | IsSquare(2*p+31)];

Mathematica

Select[Prime[Range[25000]], IntegerQ[Sqrt[2 # + 31]] &]

PARI

lista(nn) = forprime(p=2, nn, if (issquare(2*p+31), print1(p, ", "))); \\ Michel Marcus, Mar 22 2016

Python

from gmpy2 import is_prime,is_square
for p in range(3,10**6,2):
    if(not is_square(2*p+31)):continue
    elif(is_prime(p)):print(p)
# Soumil Mandal, Apr 07 2016