A283698 Numbers k such that {k^2 + 2, k^2 + 4} and {k^3 + 2, k^3 + 4} are twin prime pairs.

1, 3, 45, 2055, 39033, 48585, 101535, 104553, 112383, 117723, 129315, 152553, 170793, 178095, 234483, 246435, 258093, 272403, 304845, 306885, 365343, 372663, 375813, 405393, 405975, 436425, 456903, 494193, 538965, 551475, 559713, 569805, 570033, 767895, 792903

Offset: 1

Author

K. D. Bajpai, Mar 14 2017

Keywords

• nonn

Comments

Except a(1), all terms are multiples of 3.

a(n) == {3 or 15} (mod 30) for n>2.

Examples

			a(2) = 3, {3^2 + 2 = 11, 3^2 + 4 = 13 } and {3^3 + 2 = 29, 3^3 + 4 = 31} are twin prime pairs.
a(3) = 45, {45^2 + 2 = 2027, 45^2 + 4 = 2029 } and {45^3 + 2 = 91127, 45^3 + 4 = 91129} are twin prime pairs.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..3665 from K. D. Bajpai)

Crossrefs

Intersection of A086381 and A178337.

Cf. A000040, A144953, A173255, A178336.

Programs

Mathematica

Select[Range[1000000], PrimeQ[#^2 + 2] && PrimeQ[#^2 + 4] && PrimeQ[#^3 + 2] && PrimeQ[#^3 + 4] &]

PARI

for(n=1, 100000, if(isprime(n^2+2) && isprime(n^2+4) && isprime(n^3+2) && isprime(n^3+4), print1(n, ", ")))