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A284058 Numbers k such that {k + 2, k + 4} and {k^3 + 2, k^3 + 4} are twin prime pairs. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 25 19:19 EDT 2022. Contains 354071 sequences. (Running on oeis4.)