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Numbers m such that f(k) * 2^m - 1 is prime, where f(j) = A070826(j) and k is the number of decimal digits of 2^m.
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%I #19 Aug 03 2024 07:08:25

%S 2,3,4,6,14,17,18,23,33,43,45,53,60,70,114,141,162,178,387,657,787,

%T 951,1517,1882,1999,2423,2722,3635,3636,3893,5021,5631,7580,7674,8318,

%U 9479,19761

%N Numbers m such that f(k) * 2^m - 1 is prime, where f(j) = A070826(j) and k is the number of decimal digits of 2^m.

%C a(1) through a(32) have been proved to be prime with WinPFGW. a(32) has 7901 digits. No more terms up to 7300.

%C Results were computed using the PrimeFormGW (PFGW) primality-testing program. - _Hugo Pfoertner_, Nov 14 2019

%e a(5)=14 because 1155 * 2^14 - 1 = 18923519, a prime.

%t Do[ If[ PrimeQ[ Product[ Prime[i], {i, Floor[ n / Log[2, 10] + 1]}] * 2^(n - 1) - 1], Print[n]], {n, 7300}] (* _Robert G. Wilson v_, Jul 23 2004 *)

%K more,nonn,base

%O 1,1

%A _Jason Earls_, Jul 18 2004

%E Edited by _Robert G. Wilson v_, Jul 23 2004

%E a(33)-a(37) from _Michael S. Branicky_, Aug 03 2024