A111504 Numbers k such that k^5 - k^3 - 1 and k^5 - k^3 + 1 are twin primes.

5, 6, 64, 210, 265, 364, 440, 475, 546, 625, 680, 785, 806, 839, 925, 930, 931, 951, 1044, 1091, 1105, 1224, 1226, 1559, 1636, 1651, 1699, 1835, 1850, 1966, 1995, 2120, 2295, 2309, 2511, 2541, 2655, 2984, 3100, 3501, 3680, 4159, 4444, 4474, 4580, 4606, 4755, 4779

Offset

1,1

Links

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

Example

5^5 - 5^3 - 1 = 2999, 5^5 - 5^3 + 1 = 3001, and 2999 and 3001 are twin primes, so 5 is in the sequence.

Mathematica

lst={}; Do[If[PrimeQ[n^5-n^3-1]&&PrimeQ[n^5-n^3+1], AppendTo[lst, n]], {n, 10^3}]; lst (* Vladimir Joseph Stephan Orlovsky, Aug 14 2008 *)

Prog

(Magma) [k: k in [1..4800]| IsPrime(a-1) and IsPrime(a+1) where a is k^5 - k^3]; // Marius A. Burtea, Jan 01 2020

Crossrefs

Cf. A001097, A001359, A006512.

Sequence in context: A191557 A223530 A132444 * A041057 A041058 A322844

Adjacent sequences: A111501 A111502 A111503 * A111505 A111506 A111507

Keyword

nonn

Author

Pierre CAMI, Nov 16 2005

Extensions

3 missing terms added by Amiram Eldar, Jan 01 2020

Status

approved