A269666 Prime sums of five Mersenne primes.

19, 23, 31, 43, 47, 59, 71, 79, 83, 103, 107, 127, 131, 139, 151, 167, 179, 199, 223, 227, 251, 263, 271, 347, 419, 443, 8219, 8231, 8243, 8263, 8287, 8291, 8363, 8387, 8699, 16427, 16447, 16451, 16519, 16547, 16763, 24611, 32771, 131111, 131143, 131171

Offset: 1

Author

Robert Israel, Mar 02 2016

Keywords

• nonn

Comments

Primes of the form A000668(i_1) + ... + A000668(i_5), i_1 <= i_2 <= ... <= i_5.

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.

Examples

			a(1) = 3 + 3 + 3 + 3 + 7 = 19.
a(2) = 3 + 3 + 3 + 7 + 7 = 23.
a(3) = 3 + 7 + 7 + 7 + 7 = 31.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..368

Crossrefs

Cf. A000668, A174056.

Programs

Maple

N:= 10^10: # to get all terms <= N
for n from 1 while numtheory:-mersenne([n]) < N do od:
S:= {seq(numtheory:-mersenne([i]),i=1..n-1)}:
sort(select(t -> (t <= N and isprime(t)), convert(
{seq(seq(seq(seq(seq(S[i]+S[j]+S[k]+S[l]+S[m],
  m=1..l),l=1..k),k=1..j),j=1..i),i=1..n-1)},list)));

Mathematica

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 *)