A243472 Primes p such that p^6 - p^5 - 1 is prime.
2, 31, 101, 151, 181, 199, 229, 277, 307, 317, 379, 439, 479, 491, 647, 691, 797, 911, 997, 1039, 1051, 1181, 1291, 1367, 1381, 1471, 1511, 1549, 1657, 1709, 1847, 1867, 1987, 2081, 2099, 2111, 2207, 2467, 2621, 2707, 3041, 3221, 3259, 3541, 3571, 3581, 3769
Offset: 1
Keywords
Examples
31 appears in the sequence because it is prime and 31^6 - 31^5 - 1 = 858874529 is also prime. 101 appears in the sequence because it is prime and 101^6 - 101^5 - 1 = 1051010050099 is also prime.
Links
- K. D. Bajpai, Table of n, a(n) for n = 1..4699
Programs
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Maple
A243472 := proc() local a, b; a:=ithprime(n); b:= a^6-a^5-1; if isprime (b) then RETURN (a); fi; end: seq(A243472 (), n=1..2000);
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Mathematica
c = 0; Do[k=Prime[n]; If[PrimeQ[k^6-k^5-1], c++; Print[c," ",k]], {n,1,200000}]; Select[Prime[Range[600]],PrimeQ[#^6-#^5-1]&] (* Harvey P. Dale, Jan 21 2015 *) -
PARI
s=[]; forprime(p=2, 4000, if(isprime(p^6-p^5-1), s=concat(s, p))); s \\ Colin Barker, Jun 06 2014