A013159 -id:A013159 - cp's OEIS frontend

A178336 Smaller member of a twin prime pair of the form (k^3 + 2, k^3 + 4).

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

nonn

			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

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)

Cf. A013159, A053703, A132282, A144953, A173255, A178228.

Select[Range[3100]^3+2,PrimeQ[#]&&PrimeQ[#+2]&] (* Harvey P. Dale, May 26 2012 *)

a(n) = A178337(n)^3 + 2.

Keyword:base removed, 2 missing terms inserted by R. J. Mathar, Jun 27 2010

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

Original entry on oeis.org

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

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

nonn

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.

			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.

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

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

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

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

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

cp's OEIS Frontend

A178336 Smaller member of a twin prime pair of the form (k^3 + 2, k^3 + 4).

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