%I #18 Sep 08 2022 08:45:21
%S 5,6,64,210,265,364,440,475,546,625,680,785,806,839,925,930,931,951,
%T 1044,1091,1105,1224,1226,1559,1636,1651,1699,1835,1850,1966,1995,
%U 2120,2295,2309,2511,2541,2655,2984,3100,3501,3680,4159,4444,4474,4580,4606,4755,4779
%N Numbers k such that k^5 - k^3 - 1 and k^5 - k^3 + 1 are twin primes.
%H Amiram Eldar, <a href="/A111504/b111504.txt">Table of n, a(n) for n = 1..10000</a>
%e 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.
%t 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 *)
%o (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
%Y Cf. A001097, A001359, A006512.
%K nonn
%O 1,1
%A _Pierre CAMI_, Nov 16 2005
%E 3 missing terms added by _Amiram Eldar_, Jan 01 2020