A245639 Prime numbers P such that 8*P^2-1 is also prime.

2, 3, 5, 11, 17, 19, 23, 31, 59, 67, 79, 89, 103, 107, 137, 173, 193, 229, 233, 241, 257, 263, 271, 311, 317, 353, 359, 383, 409, 431, 479, 509, 521, 523, 541, 563, 569, 577, 593, 599, 613, 641, 709, 739, 751, 787, 829, 887, 907, 919, 947, 971, 983, 1033

Offset

1,1

Links

Pierre CAMI, Table of n, a(n) for n = 1..10000

Example

8*2^2-1=31 prime so a(1)=2.
8*3^2-1=71 prime so a(2)=3.
8*5^2-1=199 prime so a(3)=5.
8*7^2-1=391 composite.
8*11^2-1=967 prime so a(4)=11.

Mathematica

Reap[Do[p = Prime[n]; If[PrimeQ[8*p^2-1], Sow[p]], {n, 1, 200}]][[2, 1]] (* Jean-François Alcover, Jul 28 2014 *)
Select[Prime[Range[200]], PrimeQ[8 #^2 - 1] &] (* Vincenzo Librandi, Sep 07 2014 *)

Prog

(PFGW & SCRIPT)
SCRIPT
DIM n, 0
DIMS t
OPENFILEOUT myf, a(n).txt
LABEL loop1
SET n, n+1
SETS t, %d, %d\,; n; p(n)
PRP 8*p(n)^2-1, t
IF ISPRP THEN GOTO a
GOTO loop1
LABEL a
WRITE myf, t
GOTO loop1
(PARI) select(p->isprime(8*p^2-1), primes(300)) \\ Colin Barker, Jul 28 2014
(Python)
import sympy
from sympy import isprime
from sympy import prime
for n in range(1, 10**3):
..p = prime(n)
..if isprime(8*p**2-1):
....print(p, end=', ')
# Derek Orr, Aug 13 2014
(Magma) [p: p in PrimesUpTo(1500)| IsPrime(8*p^2-1)]; // Vincenzo Librandi, Sep 07 2014

Crossrefs

Cf. A245640, A245641, A245642, A245643.

Sequence in context: A220627 A040083 A045308 * A362239 A147813 A338578

Adjacent sequences: A245636 A245637 A245638 * A245640 A245641 A245642

Keyword

nonn,easy

Author

Pierre CAMI, Jul 28 2014

Status

approved