A156021 Numbers k such that k^1 + k^2 + k^3 + k^4 -+ 1 are twin primes.
1, 2, 12, 30, 44, 50, 63, 74, 110, 165, 177, 222, 239, 254, 327, 492, 519, 804, 942, 954, 1007, 1343, 1352, 1520, 1770, 2375, 2450, 2658, 2795, 2945, 2994, 3075, 3332, 3527, 3548, 3803, 3915, 3935, 4025, 4653, 4704, 4785, 4808, 4862, 5270, 5310, 5364, 5370
Offset: 1
Examples
2 is a term since 2 + 2^2 + 2^3 + 2^4 - 1 = 29 and 2 + 2^2 + 2^3 + 2^4 + 1 = 31 are twin primes.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Programs
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Magma
[n: n in [1..6*10^3] | IsPrime(n^4+n^3+n^2+n-1) and IsPrime(n^4+n^3+n^2+n+1)]; // Vincenzo Librandi, Dec 26 2015
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Mathematica
lst={};Do[p=(n^1+n^2+n^3+n^4);If[PrimeQ[p-1]&&PrimeQ[p+1],AppendTo[lst,n]],{n,8!}];lst