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
Examples
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.
Links
- Pierre CAMI, Table of n, a(n) for n = 1..10000
Programs
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Magma
[p: p in PrimesUpTo(1500)| IsPrime(8*p^2-1)]; // Vincenzo Librandi, Sep 07 2014
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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 *) -
PARI
select(p->isprime(8*p^2-1), primes(300)) \\ Colin Barker, Jul 28 2014
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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