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Numbers k such that 5^k + 2 is a prime.
14

%I #45 Jun 06 2021 17:19:02

%S 0,1,3,17,143,261,551,2285,18731,18995,19751,62067,98051,169727,442281

%N Numbers k such that 5^k + 2 is a prime.

%C Terms <= 551 correspond to certified primes.

%C a(15) > 2*10^5. - _Robert Price_, Jan 16 2015

%H Henri & Renaud Lifchitz, <a href="http://www.primenumbers.net/prptop/searchform.php?form=5%5En%2B2&amp;action=Search">PRP Records</a>.

%e a(3)=3 is a term because 5^3 + 2 = 127 is a prime.

%e 5^17 + 2 = 762939453127 is prime, hence 17 is a term.

%t Do[If[PrimeQ[5^n + 2], Print[n]], {n, 1, 10000}] (* _Ryan Propper_, Jun 17 2005 *)

%o (PARI) for(n=0, 10^5, if(ispseudoprime(5^n+2), print1(n, ", "))) \\ _Felix Fröhlich_, Jun 04 2014

%Y Cf. A051783 (3^n + 2 is prime).

%K hard,nonn

%O 1,3

%A _Donald S. McDonald_, Oct 13 2003

%E a(7)-a(8) from _Ryan Propper_, Jun 17 2005

%E a(9)-a(12) found by Mike Oakes in 2003. - _Alexander Adamchuk_, Mar 02 2008

%E Edited by _Ray Chandler_, Jul 27 2011

%E a(13) from _Ray Chandler_, Jul 28 2011

%E a(14) from _Robert Price_, Jan 16 2015

%E a(15) from _Paul Bourdelais_, Jan 28 2021