A224781 Primes p such that both 2*p + 1 and p^2 + p + 1 are primes.

2, 3, 5, 41, 89, 131, 173, 293, 743, 761, 911, 1559, 1583, 1811, 1931, 1973, 2129, 2273, 2339, 2969, 3449, 3491, 4409, 4733, 5003, 5039, 5501, 6173, 6551, 6761, 7883, 7901, 8093, 8741, 9059, 9689, 10589, 10781, 11171, 11549, 13229, 13553, 14939, 15569

Offset

1,1

Comments

Intersection of A005384 and A053182.

Note that 2p+1 is the derivative of p^2+p+1 with respect to p. - T. D. Noe, Apr 18 2013

Links

Table of n, a(n) for n=1..44.

Example

5 is a member since 5+6=11 and 5*6+1=31 are both primes.

Mathematica

Select[Prime[Range[1850]], PrimeQ[2*# + 1] && PrimeQ[#^2 + # + 1] &]

Crossrefs

Cf. A005384, A053182.

Sequence in context: A088483 A235681 A322748 * A136015 A106713 A106820

Adjacent sequences: A224778 A224779 A224780 * A224782 A224783 A224784

Keyword

nonn

Author

Jayanta Basu, Apr 17 2013

Status

approved