A297306 Primes p such that q = 4*p+1 and r = (2*p+1)/3 are also primes.

7, 43, 79, 163, 673, 853, 919, 1063, 1429, 1549, 1663, 2143, 2683, 3229, 3499, 4993, 5119, 5653, 5779, 6229, 6343, 7333, 7459, 7669, 8353, 8539, 8719, 9829, 10009, 10243, 10303, 11383, 11689, 12583, 13399, 14149, 14653, 14923, 15649, 16603, 17053, 17389, 17749

Offset

1,1

Comments

This sequence was suggested by Moshe Shmuel Newman. It has its source in his study of finite groups.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Example

Prime p = 7 is in the sequence because q = 4*7+1 = 29 and r = (2*7+1)/3 = 5 are also primes.

Maple

a:= proc(n) option remember; local p; p:= `if`(n=1, 1, a(n-1));
      do p:= nextprime(p); if irem(p, 3)=1 and
         isprime(4*p+1) and isprime((2*p+1)/3) then break fi
      od; p
    end:
seq(a(n), n=1..50);  # Alois P. Heinz, Jan 07 2018

Mathematica

a[n_] := a[n] = Module[{p}, p = If[n == 1, 1, a[n-1]]; While[True, p = NextPrime[p]; If[Mod[p, 3] == 1 && PrimeQ[4p+1] && PrimeQ[(2p+1)/3], Break[]]]; p];
Array[a, 50] (* Jean-François Alcover, Nov 27 2020, after Alois P. Heinz *)

Prog

(PARI) isok(p) = isprime(p) && isprime(4*p+1) && iferr(isprime((2*p+1)/3), E, 0); \\ Michel Marcus, Nov 27 2020

Crossrefs

Cf. A000040.

Intersection of A023212 and A104163.

Sequence in context: A052029 A168026 A142102 * A247949 A031914 A172469

Adjacent sequences: A297303 A297304 A297305 * A297307 A297308 A297309

Keyword

nonn

Author

David S. Newman, Jan 04 2018

Extensions

More terms from Alois P. Heinz, Jan 07 2018

Status

approved