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A178337 Numbers k such that (k^3 + 2, n^3 + 4) is a twin prime pair. 5
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 (list; graph; refs; listen; history; text; internal format)
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 A079038 A101790

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

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Last modified October 19 11:32 EDT 2020. Contains 337880 sequences. (Running on oeis4.)