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URL: https://oeis.org/A245639

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A245639
Prime numbers P such that 8*P^2-1 is also prime.
5
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
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
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
KEYWORD
nonn,easy
AUTHOR
Pierre CAMI, Jul 28 2014
STATUS
approved