A236692 Numbers k such that k+1, 2*k+1 and k^2+1 are primes.

1, 2, 6, 36, 156, 210, 270, 306, 576, 690, 936, 966, 2136, 2310, 2550, 2706, 2850, 3390, 3966, 4026, 4176, 4260, 4566, 4590, 5226, 5430, 5850, 6120, 6216, 6360, 6420, 6546, 7410, 7536, 8940, 9126, 9240, 9276, 9900, 10530, 10836, 11286, 11586, 11886, 12390, 13680

Offset: 1

Author

Alex Ratushnyak, Jan 30 2014

Keywords

• nonn

Comments

Intersection of A070689 and {b(n)=A005382(n)-1}.

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A005382, A070689.

Programs

Mathematica

Select[Range[14000],AllTrue[{#+1,2#+1,#^2+1},PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Dec 27 2019 *)

PARI

isok(n) = isprime(n+1)&&isprime(2*n+1)&&isprime(n^2+1); \\ Colin Barker, Jan 30 2014

Python

import sympy
from sympy import isprime
for n in range(100000):
    if isprime(n+1) and isprime(n*2+1) and isprime(n*n+1): print(n, end=', ')