A357199 Primes p such that (5*p+2)/3 is the square of a prime.

2, 5, 29, 101, 173, 317, 821, 1109, 2693, 4133, 6869, 9677, 11261, 17957, 22349, 29837, 32573, 60293, 68141, 83477, 128621, 164117, 186149, 190181, 221069, 225461, 343829, 406397, 440669, 467813, 526781, 561053, 579773, 716789, 748613, 845381, 853949, 888653, 1131077, 1214957, 1326701, 1647389

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(3) = 29 is a term because (5*29+2)/3 = 49 = 7^2 where 29 and 7 are prime.

Maple

R:= NULL: count:= 0:
q:= 1:
while count < 100 do
  q:= nextprime(q);
  if member(q mod 5, {2, 3}) then
    p := (3*q^2-2)/5;
    if isprime(p) then
      R:= R, p; count:= count+1
    fi
  fi
od:
R;

Prog

(PARI) isok(p) = if (isprime(p), my(x=(5*p+2)/3, q); issquare(x, &q) && isprime(q)); \\ Michel Marcus, Sep 25 2022

Crossrefs

Sequence in context: A083472 A213996 A057794 * A257545 A073715 A104083

Adjacent sequences: A357196 A357197 A357198 * A357200 A357201 A357202

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Sep 18 2022

Status

approved