cp's OEIS Frontend

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

%I A166484 #25 Apr 03 2023 10:36:11
%S A166484 11,13,23,37,263,277,65543,65557,4295032837
%N A166484 Prime sums of three Fermat numbers: primes of form 2^2^x + 2^2^y + 5.
%C A166484 One can have a prime sum of two Fermat Primes, starting with 2 + 3 = 5.
%C A166484 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.
%C A166484 According to the Maple 9 primality test, the next term is larger than 10^300 if it exists. - _R. J. Mathar_, Oct 16 2009
%C A166484 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.
%C A166484 The next term, if it exists, has at least 1262612 digits. - _Arkadiusz Wesolowski_, Mar 06 2011
%H A166484 G. L. Honaker, Jr. and Chris Caldwell, <a href="https://t5k.org/curios/cpage/9412.html">Prime Curios! 65557</a>
%F A166484 A155877 INTERSECTION A000040.
%F A166484 {p = (2^(2^a) + 1) + (2^(2^b) + 1) + (2^(2^c) + 1) for nonnegative integers a, b, c, such that p is prime}.
%e A166484 a(1) = A000215(0) + A000215(0) + A000215(1) = 3 + 3 + 5 = 11, which is prime.
%e A166484 a(2) = A000215(0) + A000215(1) + A000215(1) = 3 + 5 + 5 = 13, which is prime.
%e A166484 a(3) = A000215(0) + A000215(0) + A000215(2) = 3 + 3 + 17 = 23, which is prime.
%e A166484 a(4) = A000215(0) + A000215(2) + A000215(2) = 3 + 17 + 17 = 37, which is prime.
%o A166484 (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
%Y A166484 Cf. A000040, A155877, A019434.
%K A166484 hard,nonn
%O A166484 1,1
%A A166484 _Jonathan Vos Post_, Oct 14 2009, Oct 22 2009
%E A166484 a(9) from _R. J. Mathar_, Oct 16 2009
%E A166484 Definition improved by _Arkadiusz Wesolowski_, Feb 16 2011