A269787 Primes p such that 2*p + 43 is a square.

3, 19, 199, 523, 739, 991, 1279, 2791, 3259, 6823, 9091, 12619, 13591, 15643, 17839, 32491, 34039, 37243, 40591, 63703, 68059, 72559, 79579, 86923, 89443, 105319, 110899, 137791, 144163, 153991, 160723, 171091, 178183, 192799, 196543, 200323, 211879, 219763

Offset: 1

Author

Vincenzo Librandi, Mar 22 2016

Keywords

• nonn

Comments

Primes of the form 2*k^2 + 2*k - 21.

Crossrefs

Cf. A000040.

Subsequence of A002145, A045409.

Cf. similar sequences listed in A269784.

Programs

Magma

[p: p in PrimesUpTo(300000) | IsSquare(2*p + 43)];

Mathematica

Select[Prime[Range[25000]], IntegerQ[Sqrt[2 # + 43]] &]

PARI

lista(nn) = forprime(p=2, nn, if (issquare(2*p+43), 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+43)):continue
    elif(is_prime(p)):print(p)
# Soumil Mandal, Apr 07 2016