A269785 Primes p such that 2*p + 23 is a square.

13, 29, 73, 101, 353, 409, 601, 673, 829, 1093, 1289, 1613, 1973, 2801, 2953, 3109, 3433, 4129, 4889, 5501, 6373, 6833, 7069, 7309, 8053, 9649, 9929, 10501, 13933, 16369, 18229, 19001, 20593, 21001, 25301, 26209, 26669, 28549, 30493, 31489, 33013, 33529, 36709

Offset: 1

Author

Vincenzo Librandi, Mar 22 2016

Keywords

• nonn

Comments

Primes of the form 2*k^2 + 2*k - 11.

Crossrefs

Cf. A000040.

Subsequence of A002144, A045433.

Cf. similar sequences listed in A269784.

Programs

Magma

[p: p in PrimesUpTo(50000) | IsSquare(2*p + 23)];

Mathematica

Select[Prime[Range[5000]], IntegerQ[Sqrt[2 # + 23]] &]

PARI

lista(nn) = forprime(p=2, nn, if (issquare(2*p+23), 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+23)):continue
    elif(is_prime(p)):print(p)
# Soumil Mandal, Apr 07 2016