A236193 Primes p with prime(p)^2 + (2*p)^2 and p^2 + (2*prime(p))^2 both prime.

3, 139, 179, 233, 491, 929, 1217, 1429, 1597, 1613, 1987, 2243, 3061, 3499, 3529, 4507, 5737, 5779, 6329, 7247, 7823, 8263, 8839, 9941, 10259, 11317, 11383, 12157, 12421, 13093, 13219, 13367, 14449, 14669, 15101, 15877, 17449, 18523, 18593, 19051

Offset

1,1

Comments

By part (i) of the conjecture in A236192, this sequence should have infinitely many terms.

Links

Zhi-Wei Sun, Table of n, a(n) for n = 1..10000

Example

a(1) = 3 since prime(2)^2 + (2*2)^2 = 25 is composite, but prime(3)^2 + (2*3)^2 = 5^2 + 6^2 = 61 and 3^2 + (2*prime(3))^2 = 3^2 + 10^2 = 109 are both prime.

Mathematica

p[n_]:=PrimeQ[Prime[n]^2+(2*n)^2]&&PrimeQ[n^2+(2*Prime[n])^2]
n=0; Do[If[p[Prime[k]], n=n+1; Print[n, " ", Prime[k]]], {k, 1, 10^6}]

Crossrefs

Cf. A000040, A236119, A236143, A236192.

Sequence in context: A049677 A030247 A139956 * A070322 A053527 A195632

Adjacent sequences: A236190 A236191 A236192 * A236194 A236195 A236196

Keyword

nonn

Author

Zhi-Wei Sun, Jan 20 2014

Status

approved