

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
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OFFSET

1,2


COMMENTS

With the exception of k = 1, all k are odd multiples of 3 with a leastsignificant 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,changed


AUTHOR

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


EXTENSIONS

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


STATUS

approved



