A224781 - OEIS

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

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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] &]