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%I #21 Apr 03 2023 10:36:13
%S 41,137,2147483777,162259895799233006081715459850241
%N Prime sums of three distinct Mersenne primes (A000668).
%C 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
%C a(5) > 10^30000, if it exists. - _Jinyuan Wang_, Jul 26 2021
%H Chris K. Caldwell and G. L. Honaker, Jr., <a href="https://t5k.org/curios/page.php?curio_id=27433">16225...50241 (33-digits)</a>, Prime Curios!
%e a(3) = 2147483777 because 2147483777 = (2^2-1) + (2^7-1) + (2^31-1).
%t 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 *)
%Y Cf. A000040, A000043, A000668, A174056.
%K nonn,hard
%O 1,1
%A _G. L. Honaker, Jr._, Jan 08 2015