A128066 - OEIS

%I #20 Jan 22 2019 03:51:32

%S 3,5,19,37,173,211,227,619,977,1237,2437,5741,13463,23929,81223,121271

%N Numbers k such that (3^k + 4^k)/7 is prime.

%C All terms are primes.

%H Henri Lifchitz & Renaud Lifchitz, <a href="http://www.primenumbers.net/prptop/searchform.php?form=%284%5Ep%2B3%5Ep%29%2F7">Top probable primes of the form (4^p+3^p)/7</a>

%p a:=proc(n) if type((3^n+4^n)/7,integer)=true and isprime((3^n+4^n)/7)=true then n else fi end: seq(a(n),n=1..1500); # _Emeric Deutsch_, Feb 17 2007

%t Do[ p=Prime[n]; f=(3^p+4^p)/(4+3); If[ PrimeQ[f], Print[p]], {n,1,100} ]

%o (PARI) f(n)=(3^n + 4^n)/7;

%o forprime(n=3,10^5,if(ispseudoprime(f(n)),print1(n,", ")))

%o /* _Joerg Arndt_, Mar 27 2011 */

%Y Cf. A007658 = n such that (3^n + 1)/4 is prime; A057469 ((3^n + 2^n)/5); A122853 ((3^n + 5^n)/8).

%Y Cf. A128067, A128068, A128069, A128070, A128071, A128072, A128073, A128074, A128075.

%Y Cf. A059801 (4^n - 3^n); A121877 ((5^n - 3^n)/2).

%Y Cf. A128024, A128025, A128026, A128027, A128028, A128029, A128030, A128031, A128032.

%K hard,more,nonn

%O 1,1

%A _Alexander Adamchuk_, Feb 14 2007

%E 3 more terms from _Emeric Deutsch_, Feb 17 2007

%E 2 more terms from _Farideh Firoozbakht_, Apr 16 2007

%E Two more terms (13463 and 23929) found by Lelio R Paula in 2008 corresponding to probable primes with 8105 and 14406 digits. _Jean-Louis Charton_, Oct 06 2010

%E Two more terms (81223 and 121271) found by Jean-Louis Charton in March 2011 corresponding to probable primes with 48901 and 73012 digits