A253682 Prime sums of three distinct Mersenne primes (A000668).

41, 137, 2147483777, 162259895799233006081715459850241

Offset: 1

Author

G. L. Honaker, Jr., Jan 08 2015

Keywords

• nonn
• hard

Comments

a(1) has the exponents of the three distinct Mersenne primes of 1, 2 and 3; a(2) the exponents are 1, 2 and 4, a(3) the exponents are 1, 4 and 8 and a(4) the exponents are 1, 10 and 11. - Robert G. Wilson v, Jan 08 2015

a(5) > 10^30000, if it exists. - Jinyuan Wang, Jul 26 2021

Examples

			a(3) = 2147483777 because 2147483777 = (2^2-1) + (2^7-1) + (2^31-1).
		

Links

• Chris K. Caldwell and G. L. Honaker, Jr., 16225...50241 (33-digits), Prime Curios!

Crossrefs

Cf. A000040, A000043, A000668, A174056.

Programs

Mathematica

exp={* the first 34 terms in A000043 *}; Do[ s = 2^exp[[p]] + 2^exp[[q]] + 2^exp[[r]] - 3; If[ PrimeQ@ s, Print[{p, q, r, s}]], {r, 3, 34}, {q, 2, r - 1}, {p, q - 1}] (* Robert G. Wilson v, Jan 08 2015 *)