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A283698 Numbers k such that {k^2 + 2, k^2 + 4} and {k^3 + 2, k^3 + 4} are twin prime pairs. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 29 18:11 EST 2021. Contains 349416 sequences. (Running on oeis4.)