A237995 Primes p such that p^4 - p^3 - 1 is also prime.

2, 3, 5, 11, 17, 53, 59, 101, 103, 151, 157, 167, 193, 197, 239, 353, 379, 397, 419, 433, 467, 479, 503, 599, 641, 659, 661, 743, 787, 881, 907, 911, 983, 1049, 1109, 1123, 1153, 1201, 1229, 1291, 1307, 1373, 1399, 1429, 1531, 1601, 1621, 1663, 1747, 1753

Offset

1,1

Links

K. D. Bajpai, Table of n, a(n) for n = 1..3700

Example

5 is in the sequence because 5 is prime and 5^4 - 5^3 - 1 = 499 is also prime.
17 is in the sequence because 17 is prime and 17^4 - 17^3 - 1 = 78607 is also prime.

Maple

KD := proc() local a, b; a:= ithprime(n); b:= a^4-a^3-1; if isprime(b) then RETURN (a); fi; end: seq(KD(), n=1..400);

Mathematica

c = 0; a = 2; Do[k = Prime[n]; If[PrimeQ[k^4 - k^3 - 1], c = c + 1;  Print[c, " ", k]], {n, 100000}]; (* Bajpai *)
Select[Prime[Range[200]], PrimeQ[#^4 - #^3 - 1] &] (* Alonso del Arte, Feb 17 2014 *)

Prog

(PARI) s=[]; forprime(p=2, 2000, if(isprime(p^4-p^3-1), s=concat(s, p))); s \\ Colin Barker, Feb 17 2014

Crossrefs

Cf. A000040, A237639, A237641, A237642.

Sequence in context: A007755 A060611 A077497 * A333081 A178606 A097048

Adjacent sequences: A237992 A237993 A237994 * A237996 A237997 A237998

Keyword

nonn

Author

K. D. Bajpai, Feb 16 2014

Status

approved