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%I #17 Mar 03 2016 10:49:41
%S 19,23,31,43,47,59,71,79,83,103,107,127,131,139,151,167,179,199,223,
%T 227,251,263,271,347,419,443,8219,8231,8243,8263,8287,8291,8363,8387,
%U 8699,16427,16447,16451,16519,16547,16763,24611,32771,131111,131143,131171
%N Prime sums of five Mersenne primes.
%C Primes of the form A000668(i_1) + ... + A000668(i_5), i_1 <= i_2 <= ... <= i_5.
%C There are 368 terms up to 10^1000, 13 more up to 10^1332, none between 10^1332 and 10^2916, and 9 between 10^2916 and 10^3000. Conjecture: the sequence is finite.
%H Robert Israel, <a href="/A269666/b269666.txt">Table of n, a(n) for n = 1..368</a>
%e a(1) = 3 + 3 + 3 + 3 + 7 = 19.
%e a(2) = 3 + 3 + 3 + 7 + 7 = 23.
%e a(3) = 3 + 7 + 7 + 7 + 7 = 31.
%p N:= 10^10: # to get all terms <= N
%p for n from 1 while numtheory:-mersenne([n]) < N do od:
%p S:= {seq(numtheory:-mersenne([i]),i=1..n-1)}:
%p sort(select(t -> (t <= N and isprime(t)), convert(
%p {seq(seq(seq(seq(seq(S[i]+S[j]+S[k]+S[l]+S[m],
%p m=1..l),l=1..k),k=1..j),j=1..i),i=1..n-1)},list)));
%t s = {3, 7, 31, 127, 8191, 131071, 524287} (* A000668 *); Take[Union@ Flatten@ Table[p = s[[a]] + s[[b]] + s[[c]] + s[[d]] + s[[e]]; If[ PrimeQ@ p, p, Sequence @@ {}], {e, 7}, {d, e}, {c, d}, {b, c}, {a, b}], 50] (* _Robert G. Wilson v_, Mar 02 2016 *)
%Y Cf. A000668, A174056.
%K nonn
%O 1,1
%A _Robert Israel_, Mar 02 2016
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