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%I #14 Feb 12 2023 14:25:27
%S 1,3,31,47,83,1255,39015
%N Numbers k such that 7^k + 3 is semiprime.
%C Or (7^k + 3)/2 is prime.
%C a(7) > 18000. - _Jinyuan Wang_, Mar 04 2020
%C a(8) > 120000. - _Tyler Busby_, Feb 12 2023
%e 7^1 + 3 = 19 = 2*5,
%e 7^3 + 3 = 346 = 2*173,
%e 7^31 + 3 = 2*78887691017422903307521373,
%e 7^47 + 3 = 2*2621669158378151817230729359430975727773,
%e 7^83 + 3 = 2*6951960974910262341699296037696359556850100616048572362472005937832173.
%t Do[ If[ PrimeQ[(7^n + 3)/2], Print@n], {n, 1, 11501, 2}] (* _Robert G. Wilson v_, Jun 14 2006 *)
%o (PARI) is(k) = ispseudoprime((7^k+3)/2); \\ _Jinyuan Wang_, Mar 04 2020
%K nonn,more,less
%O 1,2
%A _Zak Seidov_, Jun 14 2006
%E a(6) from _Robert G. Wilson v_, Jun 14 2006
%E a(7) from _Tyler Busby_, Feb 12 2023