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

Author

K. D. Bajpai, Mar 19 2017

Keywords

• nonn

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

Examples

			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.
		

Links

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

Crossrefs

Intersection of A256388 and A178337.

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

Programs

Mathematica

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

PARI

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