A154431 - OEIS

%I #11 Sep 08 2022 08:45:40

%S 2,3,7,17,19,29,43,73,107,199,229,359,397,409,443,449,479,563,593,607,

%T 617,677,787,887,953,1013,1069,1087,1109,1213,1277,1279,1283,1367,

%U 1409,1549,1613,1627,1667,1759,1867,1877,1993,2003,2129,2269,2297,2423,2539

%N Primes p such that 5p^2 - p + 1 is prime.

%H Vincenzo Librandi, <a href="/A154431/b154431.txt">Table of n, a(n) for n = 1..1000</a>

%e For p=2,   5p^2 - p + 1 = 19 (a prime);

%e for p=107, 5p^2 - p + 1 = 57139 (a prime);

%e for p=199, 5p^2 - p + 1 = 197807 (a prime).

%p a:= proc (n) if isprime(n) and isprime(5*n^2-n+1) then n end if end proc: seq(a(n), n = 2 .. 3000); # _Emeric Deutsch_, Jan 20 2009

%t Select[Prime[Range[1000]], PrimeQ[(5#^2 - # + 1)] &] (* _Vincenzo Librandi_, Oct 14 2012 *)

%o (Magma) [p: p in PrimesUpTo(3000)|IsPrime(5*p^2 - p + 1)]; // _Vincenzo Librandi_, Oct 14 2012

%Y Cf. A154432.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Jan 09 2009

%E Extended by _Emeric Deutsch_, Jan 20 2009