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A128066
Numbers k such that (3^k + 4^k)/7 is prime.
17
3, 5, 19, 37, 173, 211, 227, 619, 977, 1237, 2437, 5741, 13463, 23929, 81223, 121271
OFFSET
1,1
COMMENTS
All terms are primes.
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} ]
PROG
(PARI) f(n)=(3^n + 4^n)/7;
forprime(n=3, 10^5, if(ispseudoprime(f(n)), print1(n, ", ")))
/* Joerg Arndt, Mar 27 2011 */
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. A059801 (4^n - 3^n); A121877 ((5^n - 3^n)/2).
Sequence in context: A228471 A062594 A128027 * A273020 A148523 A148524
KEYWORD
hard,more,nonn
AUTHOR
Alexander Adamchuk, Feb 14 2007
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
STATUS
approved