A178337 Numbers k such that (k^3 + 2, n^3 + 4) is a twin prime pair.

1, 3, 45, 63, 69, 129, 363, 495, 555, 579, 885, 993, 1053, 1185, 1719, 1839, 2055, 2175, 2199, 2409, 2595, 3039, 3063, 3303, 3399, 3555, 3615, 4245, 4443, 4449, 5073, 5373, 5535, 5703, 5949, 6015, 6075, 6693, 6795, 6849, 7023, 7119, 7155, 7509, 7779, 8535

Offset

1,2

Comments

With the exception of k = 1, all k are odd multiples of 3 with a least-significant decimal digit of 3, 5 or 9.

A178336(n) gives the values of k^3 + 2.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

1^3 + 2 = 3 = prime(2) and 3+2 = prime(3) are twin primes, so n=1 is a term.
45^3 + 2 = 91127 = prime(8811) and 91127+2 = prime(8812) are twin primes, so 45 is a term.
10893^3 + 2 = 1292535591959 = prime(48144179941) is a lower twin prime, so 10893 is a term.

Mathematica

seqQ[n_] := And @@ PrimeQ[n^3 + 3 + {-1, 1}]; Select[Range[8535], seqQ] (* Amiram Eldar, Jan 11 2020*)

Prog

(Magma) [n: n in [0..9000] | IsPrime(n^3+2) and IsPrime(n^3+4)]; // Vincenzo Librandi, Nov 18 2010

Crossrefs

Cf. A013159, A053703, A132282, A144953, A173255, A178336.

Sequence in context: A103980 A101236 A119182 * A161589 A360966 A079038

Adjacent sequences: A178334 A178335 A178336 * A178338 A178339 A178340

Keyword

nonn

Author

Ulrich Krug (leuchtfeuer37(AT)gmx.de), May 25 2010

Extensions

Keyword:base removed by R. J. Mathar, Jun 27 2010

Status

approved