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A166484
Prime sums of three Fermat numbers: primes of form 2^2^x + 2^2^y + 5.
3
11, 13, 23, 37, 263, 277, 65543, 65557, 4295032837
OFFSET
1,1
COMMENTS
One can have a prime sum of two Fermat Primes, starting with 2 + 3 = 5.
Hence this current sequence is a proper subset of prime sums of a Fermat prime number of Fermat numbers, which in turn is a proper subset of prime sums of a Fermat number of Fermat numbers.
According to the Maple 9 primality test, the next term is larger than 10^300 if it exists. - R. J. Mathar, Oct 16 2009
At least one of the three Fermat numbers must be 3 because all Fermat numbers greater than 3 are equal to 2 (mod 3). Hence, the sum of three Fermat numbers greater than 3 is always a multiple of 3.
The next term, if it exists, has at least 1262612 digits. - Arkadiusz Wesolowski, Mar 06 2011
LINKS
G. L. Honaker, Jr. and Chris Caldwell, Prime Curios! 65557
FORMULA
A155877 INTERSECTION A000040.
{p = (2^(2^a) + 1) + (2^(2^b) + 1) + (2^(2^c) + 1) for nonnegative integers a, b, c, such that p is prime}.
EXAMPLE
a(1) = A000215(0) + A000215(0) + A000215(1) = 3 + 3 + 5 = 11, which is prime.
a(2) = A000215(0) + A000215(1) + A000215(1) = 3 + 5 + 5 = 13, which is prime.
a(3) = A000215(0) + A000215(0) + A000215(2) = 3 + 3 + 17 = 23, which is prime.
a(4) = A000215(0) + A000215(2) + A000215(2) = 3 + 17 + 17 = 37, which is prime.
PROG
(PARI) for(x=1, 9, for(y=1, x, if(isprime(t=2^2^x+2^2^y+5), print1(t", ")))) \\ Charles R Greathouse IV, Apr 29 2016
CROSSREFS
KEYWORD
hard,nonn
AUTHOR
Jonathan Vos Post, Oct 14 2009, Oct 22 2009
EXTENSIONS
a(9) from R. J. Mathar, Oct 16 2009
Definition improved by Arkadiusz Wesolowski, Feb 16 2011
STATUS
approved