A128066 Numbers k such that (3^k + 4^k)/7 is prime.

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

Offset: 1

Author

Alexander Adamchuk, Feb 14 2007

Keywords

• hard
• more
• nonn

Comments

All terms are primes.

Links

• Henri Lifchitz & Renaud Lifchitz, Top probable primes of the form (4^p+3^p)/7

Crossrefs

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

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

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

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

Programs

Maple

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

Mathematica

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

PARI

f(n)=(3^n + 4^n)/7;
forprime(n=3,10^5,if(ispseudoprime(f(n)),print1(n,", ")))
/* Joerg Arndt, Mar 27 2011 */

Extensions

3 more terms from Emeric Deutsch, Feb 17 2007

2 more terms from Farideh Firoozbakht, Apr 16 2007

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

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