A181530 Greatest k <= n such that 3^n + 3^k - 1 is prime, or 0 if no such prime exists.

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, 22, 26, 21, 30, 27, 20, 35, 26, 28, 28, 35, 38, 39, 22, 37, 38, 12, 45, 39, 36, 3, 30, 49, 49, 48, 37, 28, 56, 42, 53, 17, 58, 36, 62, 59, 55, 40, 26, 64, 68, 58, 61

Offset

1,2

Links

Pierre CAMI, Table of n, a(n) for n = 1..2000

Example

For n = 4, 3^4 + 3^4 - 1 = 161 = 7*23, 3^4 + 3^3 - 1 = 107 so a(4) = 3.
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.

Prog

(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
(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

Crossrefs

Sequence in context: A036020 A036024 A036029 * A035362 A042957 A341074

Adjacent sequences: A181527 A181528 A181529 * A181531 A181532 A181533

Keyword

nonn

Author

Pierre CAMI, Jan 29 2011

Status

approved