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A121824 Primes of the form (3^n + 5^n)/2. 3

%I

%S 17,353,198593

%N Primes of the form (3^n + 5^n)/2.

%C Corresponding n are 2^1, 2^2, 2^3. What are the following terms? Cf. A074606 3^n + 5^n.

%C Since x^n + y^n has x+y as a factor if n is odd, we can assume that n is a power of 2. Maple shows that up to n = 2^15, there are no more primes of the form (3^n + 5^n)/2. This raises the question: Is it true that x^n + (x+2)^n is irreducible over Q for n a power of 2? - _W. Edwin Clark_, Sep 10 2006

%C Next term, if it exists, is > (3^2500+5^2500)/2. - _Hugo Pfoertner_, Sep 10 2006

%C No more terms <= (3^(2^17)+5^(2^17))/2=(3^131072+5^131072)/2. Hence the next term, if it exists, is greater than 10^91616 (so is too large to include). - Herman Jamke (hermanjamke(AT)fastmail.fm), Dec 31 2007

%o (PARI) for(n=1,17, m=(3^(2^n)+5^(2^n))/2;if(isprime(m),print1(m","))) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), Dec 31 2007

%Y Cf. A074606, A121710.

%K hard,nonn,bref

%O 1,1

%A _Zak Seidov_, Aug 27 2006

%E Edited by _N. J. A. Sloane_, Jan 13 2008

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Last modified September 24 07:28 EDT 2020. Contains 337317 sequences. (Running on oeis4.)