A174056 Prime sums of three Mersenne primes. Primes in A174055.

13, 17, 37, 41, 137, 257, 2147483777, 162259895799233006081715459850241

Offset

1,1

Comments

Sums of five Mersenne primes can also be prime (though, obviously sums of an even number of Mersenne primes are even).

3 + 3 + 3 + 3 + 7 = 19

3 + 3 + 3 + 7 + 7 = 23

3 + 7 + 7 + 7 + 7 = 31

3 + 3 + 3 + 3 + 31 = 43

3 + 3 + 3 + 7 + 31 = 47

7 + 7 + 7 + 7 + 31 = 59

3 + 3 + 3 + 31 + 31 = 71

3 + 7 + 7+ 31 + 31 = 79

That sequence of sums of five Mersenne primes 19, 23, 31, 43, 47, 59, 71, 79, ... is A269666.

No other terms < 10^1000. Conjecture: these are all the terms. - Robert Israel, Mar 02 2016

Links

Table of n, a(n) for n=1..8.

Formula

A000668(i) + A000668(j) + A000668(k), with integers i,j,k not necessarily distinct. The supersequence of sums of three Mersenne primes is A174055.

Example

a(1) = 3 + 3 + 7 = 13. a(2) = 3 + 7 + 7 = 17. a(3) = 3 + 3 + 31 = 37. a(4) = 3 + 7 + 31 = 41. a(5) = 3 + 7 + 127 = 137. a(6) = 3 + 127 + 127 = 257.

Maple

N:= 10^1000: # 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(isprime, convert(select(`<=`, {seq(seq(seq(s+t+u, s=S), t=S), u=S)}, N), list))); # Robert Israel, Mar 02 2016

Mathematica

Select[Total/@Tuples[Table[2^MersennePrimeExponent[n]-1, {n, 20}], 3], PrimeQ]//Union (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Sep 22 2020 *)

Crossrefs

Cf. A000668, A171251, A171252, A171253, A171254, A171255, A174055, A174057, A269666.

Cf. A155877 (sums of three Fermat numbers).

Cf. A166484 (prime sums of three Fermat numbers).

Sequence in context: A069485 A263725 A340053 * A307894 A322472 A166681

Adjacent sequences: A174053 A174054 A174055 * A174057 A174058 A174059

Keyword

more,nonn

Author

Jonathan Vos Post, Mar 06 2010

Extensions

a(7)-a(8) from Donovan Johnson, Dec 22 2010

Status

approved