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%I #15 Sep 08 2022 08:45:53
%S 1,3,45,63,69,129,363,495,555,579,885,993,1053,1185,1719,1839,2055,
%T 2175,2199,2409,2595,3039,3063,3303,3399,3555,3615,4245,4443,4449,
%U 5073,5373,5535,5703,5949,6015,6075,6693,6795,6849,7023,7119,7155,7509,7779,8535
%N Numbers k such that (k^3 + 2, n^3 + 4) is a twin prime pair.
%C With the exception of k = 1, all k are odd multiples of 3 with a least-significant decimal digit of 3, 5 or 9.
%C A178336(n) gives the values of k^3 + 2.
%H Amiram Eldar, <a href="/A178337/b178337.txt">Table of n, a(n) for n = 1..10000</a>
%e 1^3 + 2 = 3 = prime(2) and 3+2 = prime(3) are twin primes, so n=1 is a term.
%e 45^3 + 2 = 91127 = prime(8811) and 91127+2 = prime(8812) are twin primes, so 45 is a term.
%e 10893^3 + 2 = 1292535591959 = prime(48144179941) is a lower twin prime, so 10893 is a term.
%t seqQ[n_] := And @@ PrimeQ[n^3 + 3 + {-1, 1}]; Select[Range[8535], seqQ] (* _Amiram Eldar_, Jan 11 2020*)
%o (Magma) [n: n in [0..9000] | IsPrime(n^3+2) and IsPrime(n^3+4)]; // _Vincenzo Librandi_, Nov 18 2010
%Y Cf. A013159, A053703, A132282, A144953, A173255, A178336.
%K nonn
%O 1,2
%A Ulrich Krug (leuchtfeuer37(AT)gmx.de), May 25 2010
%E Keyword:base removed by _R. J. Mathar_, Jun 27 2010