A178336
Smaller member of a twin prime pair of the form (k^3 + 2, k^3 + 4).
Original entry on oeis.org
3, 29, 91127, 250049, 328511, 2146691, 47832149, 121287377, 170953877, 194104541, 693154127, 979146659, 1167575879, 1664006627, 5079577961, 6219352721, 8678316377, 10289109377, 10633486601, 13980103931, 17474794877, 28066748321, 28736971049
Offset: 1
Ulrich Krug (leuchtfeuer37(AT)gmx.de), May 25 2010
3 = 1^3+2 = prime(2) and 5 = 1^3+4 = prime(3) are a twin prime pair, so 3 becomes the first term.
91127 = 45^3+2 = prime(8811) and 91129 = 45^3+4 = prime(8812) are a twin prime pair, so 91127 is a term.
- Edmund Landau, Handbuch der Lehre von der Verteilung der Primzahlen, Band I, B. G. Teubner, Leipzig u. Berlin, 1909
Keyword:base removed, 2 missing terms inserted by
R. J. Mathar, Jun 27 2010
A283698
Numbers k such that {k^2 + 2, k^2 + 4} and {k^3 + 2, k^3 + 4} are twin prime pairs.
Original entry on oeis.org
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
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.
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Select[Range[1000000], PrimeQ[#^2 + 2] && PrimeQ[#^2 + 4] && PrimeQ[#^3 + 2] && PrimeQ[#^3 + 4] &]
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for(n=1, 100000, if(isprime(n^2+2) && isprime(n^2+4) && isprime(n^3+2) && isprime(n^3+4), print1(n, ", ")))
A284014
Numbers k such that {k + 2, k + 4} and {k^2 + 2, k^2 + 4} are both twin prime pairs.
Original entry on oeis.org
1, 3, 15, 57, 147, 2085, 6687, 6957, 11055, 15267, 17385, 17577, 20505, 20637, 23667, 26247, 31077, 31317, 32115, 32967, 34497, 39225, 47775, 52065, 53715, 55335, 56205, 58365, 62187, 63585, 66567, 67215, 70875, 77235, 77475, 82005, 85827, 89595, 89817, 107505
Offset: 1
a(2) = 3, {3 + 2 = 5, 3 + 4 = 7} and {3^2 + 2 = 11, 3^2 + 4 = 13} are twin prime pairs.
a(3) = 15, {15 + 2 = 17, 15 + 4 = 19} and {15^2 + 2 = 227, 15^2 + 4 = 229} are twin prime pairs.
Appears to be the intersection of
A086381 and
A256388, but that may be unproven.
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[n: n in [0..100000] | IsPrime(n+2) and IsPrime(n+4) and IsPrime(n^2+2) and IsPrime(n^2+4)];
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Select[Range[1000000], PrimeQ[# + 2] && PrimeQ[# + 4] && PrimeQ[#^2 + 2] && PrimeQ[#^2 + 4] &]
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for(n=1, 100000,2; if(isprime(n+2) && isprime(n+4) && isprime(n^2+2) &&isprime(n^2+4), print1(n, ", ")))
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;; With Antti Karttunen's IntSeq-library.
(define A284014 (MATCHING-POS 1 1 (lambda (n) (and (= 1 (A010051 (+ n 2))) (= 1 (A010051 (+ n 4))) (= 1 (A010051 (+ (* n n) 2))) (= 1 (A010051 (+ (* n n) 4)))))))
;; Antti Karttunen, Apr 15 2017
A284058
Numbers k such that {k + 2, k + 4} and {k^3 + 2, k^3 + 4} are twin prime pairs.
Original entry on oeis.org
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
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.
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Select[Range[1000000], PrimeQ[# + 2] && PrimeQ[# + 4] && PrimeQ[#^3 + 2] && PrimeQ[#^3 + 4] &]
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for(n=1, 100000,2; if(isprime(n+2) && isprime(n+4) && isprime(n^3+2) && isprime(n^3+4), print1(n, ", ")))
Showing 1-4 of 4 results.
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