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A269666 Prime sums of five Mersenne primes. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A217281 A322960 A019360 * A007639 A261311 A168144

Adjacent sequences:  A269663 A269664 A269665 * A269667 A269668 A269669

KEYWORD

nonn

AUTHOR

Robert Israel, Mar 02 2016

STATUS

approved

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Last modified February 19 19:21 EST 2020. Contains 332047 sequences. (Running on oeis4.)