A284058 Numbers k such that {k + 2, k + 4} and {k^3 + 2, k^3 + 4} are twin prime pairs.

1, 3, 69, 1719, 3555, 8535, 8625, 9765, 10065, 17955, 27939, 32319, 34209, 35445, 39159, 44769, 47415, 55329, 56235, 75615, 85929, 91965, 96219, 97545, 98895, 122385, 122595, 138075, 142695, 143649, 145719, 152025, 191829, 192975, 197955, 200379, 201819, 202059

Offset

1,2

Comments

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

After a(2), all the terms are congruent to 5 or 9 (mod 10).

a(n) == {9 or 15} (mod 30) for n>2. - Robert G. Wilson v, Mar 19 2017

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..2352 from Robert G. Wilson v)

Example

a(2) = 3, {3 + 2 = 5, 3 + 4 = 7} and {3^3 + 2 = 29, 3^3 + 4 = 31} are twin prime pairs.
a(3) = 69, {69 + 2 = 71, 69 + 4 = 73} and {69^3 + 2 = 328511, 69^3 + 4 = 328513} are twin prime pairs.

Mathematica

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

Prog

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

Crossrefs

Intersection of A256388 and A178337.

Cf. A000040, A001359, A086381, A144953, A178336.

Sequence in context: A086223 A089455 A012201 * A012096 A012074 A350720

Adjacent sequences: A284055 A284056 A284057 * A284059 A284060 A284061

Keyword

nonn

Author

K. D. Bajpai, Mar 19 2017

Status

approved