A110587 Primes p such that p^2 = 6*q + 7, where q is prime.

5, 7, 11, 17, 19, 29, 37, 43, 47, 53, 61, 71, 73, 79, 89, 97, 101, 107, 109, 127, 173, 191, 199, 223, 241, 251, 263, 271, 281, 317, 367, 389, 397, 433, 439, 443, 449, 457, 461, 479, 523, 541, 569, 577, 587, 613, 631, 647, 659, 677, 683, 691, 701, 739, 757

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(n) = sqrt(A110586(n)). - Amiram Eldar, Aug 02 2024

Example

a(4) = 17 since 17^2 = 289 = 6*47 + 7.

Maple

ispower := proc(n, b) andmap(proc(w) evalb(w[2] mod b = 0) end, ifactors(n)[2]) end: a:=6: SQP||a:=[]: for z from 1 to 1 do for n from 1 to 1000 do p:=ithprime(n); m:=a*p+a+1; if ispower(m, 2) and isprime(sqrt(m)) then SQPW||a:=[op(SQP||a), sqrt(m)] fi od; od; SQP||a;

Mathematica

Select[Prime[Range[135]], PrimeQ[(#^2-7)/6] &] (* Amiram Eldar, Aug 02 2024 *)

Prog

(PARI) is(p) = isprime(p) && !((p^2-7) % 6) && isprime((p^2-7)/6); \\ Amiram Eldar, Aug 02 2024

Crossrefs

Cf. A110014, A110015, A110016, A110586.

Sequence in context: A086136 A136052 A301913 * A192281 A191065 A271658

Adjacent sequences: A110584 A110585 A110586 * A110588 A110589 A110590

Keyword

nonn,easy

Author

Walter Kehowski, Sep 13 2005

Status

approved