A166484 Prime sums of three Fermat numbers: primes of form 2^2^x + 2^2^y + 5.

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

Table of n, a(n) for n=1..9.

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

Cf. A000040, A155877, A019434.

Sequence in context: A106073 A072330 A097933 * A127043 A084952 A277048

Adjacent sequences: A166481 A166482 A166483 * A166485 A166486 A166487

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