A236692 Numbers n such that n+1, 2n+1 and n^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

1,2

Comments

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

Links

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

Mathematica

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

Prog

(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 str(n)+', ',
(PARI)
s=[]; for(n=1, 15000, if(isprime(n+1)&&isprime(2*n+1)&&isprime(n^2+1), s=concat(s, n))); s \\ Colin Barker, Jan 30 2014

Crossrefs

Cf. A005382, A070689.

Sequence in context: A127564 A130874 A019020 * A323945 A369080 A101609

Adjacent sequences: A236689 A236690 A236691 * A236693 A236694 A236695

Keyword

nonn

Author

Alex Ratushnyak, Jan 30 2014

Status

approved