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

1,1

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.

Links

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

Example

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

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 *)

Crossrefs

Cf. A000668, A174056.

Sequence in context: A322960 A348935 A019360 * A007639 A261311 A168144

Adjacent sequences: A269663 A269664 A269665 * A269667 A269668 A269669

Keyword

nonn

Author

Robert Israel, Mar 02 2016

Status

approved