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%I #29 Sep 08 2022 08:45:54
%S 1,2,3,3,3,5,7,8,6,8,8,12,7,6,12,15,8,13,13,20,18,20,23,22,20,8,27,26,
%T 22,26,21,30,27,20,35,26,28,28,35,38,39,22,37,38,12,45,39,36,3,30,49,
%U 49,48,37,28,56,42,53,17,58,36,62,59,55,40,26,64,68,58,61
%N Greatest k <= n such that 3^n + 3^k - 1 is prime, or 0 if no such prime exists.
%H Pierre CAMI, <a href="/A181530/b181530.txt">Table of n, a(n) for n = 1..2000</a>
%e For n = 4, 3^4 + 3^4 - 1 = 161 = 7*23, 3^4 + 3^3 - 1 = 107 so a(4) = 3.
%e For n = 154, for k = 0, 1, 2, 3, ..., 154, the numbers 3^154 + 3^k - 1 are respectively divisible by 3, 5531, 73, 5, 7, 19001, 6553, 5, 239, 3541, 7, 5, 33247, 71, 19, 5, 7, 29, 1973, 5, 436467739, 71161, 7, 5, 4283, 37, 73, 5, 7, 11177, 13721, 5, 19, 29207, 7, 5, 64849, 4001, 73, 5, 7, 31, 227009113, 5, 139, 29, 7, 5, 71, 107102231, 19, 5, 7, 10765021647412056860623883, 521, 5, 241, 1448445976112887644909473, 7, 5, 5657, 37, 73, 5, 7, 110661029, 65963, 5, 19, 20411, 7, 5, 331, 29, 73, 5, 7, 7671791, 269, 5, 563, 211, 7, 5, 6553, 113, 19, 5, 7, 425679689, 1301, 5, 334244063, 53, 7, 5, 15254167, 37, 73, 5, 7, 29, 3391, 5, 19, 7727, 7, 5, 4799, 2269, 73, 5, 7, 1822597729, 47, 5, 242496218184092003, 38971, 7, 5, 9994245487379630507640393493999, 9104413, 19, 5, 7, 3581, 1039, 5, 181, 29, 7, 5, 2472681219552827727900539, 37, 73, 5, 7, 47, 99986141, 5, 19, 1237, 7, 5, 55817, 53, 73, 5, 7, 1033, 9187, 5, 199, 71, 7. So a(154) = 0.
%o (PARI) a(n) = my(k=n); while (!isprime(3^n + 3^k - 1), k--; if (k==0, return (0))); k; \\ _Michel Marcus_, Sep 16 2019
%o (Magma) sol:=[];for n in [1..70] do k:=n; while not IsPrime(3^n+3^k-1) and k gt 0 do k:=k-1; end while; if k ge 0 then Append(~sol,k); else Append(~sol,0);end if; end for; sol; // _Marius A. Burtea_, Sep 16 2019
%K nonn
%O 1,2
%A _Pierre CAMI_, Jan 29 2011
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