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

1,2

Comments

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

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

Links

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

Example

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.

Mathematica

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

Prog

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

Crossrefs

Intersection of A086381 and A178337.

Cf. A000040, A144953, A173255, A178336.

Sequence in context: A072503 A154242 A331710 * A163002 A117253 A012833

Adjacent sequences: A283695 A283696 A283697 * A283699 A283700 A283701

Keyword

nonn

Author

K. D. Bajpai, Mar 14 2017

Status

approved