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 A234346 Primes of the form 3^k + 3^m - 1, where k and m are positive integers. 12
 5, 11, 17, 29, 53, 83, 89, 107, 251, 269, 809, 971, 2213, 2267, 4373, 6563, 6569, 6803, 8747, 13121, 19709, 19763, 20411, 59051, 65609, 177173, 183707, 531521, 538001, 590489, 1062881, 1594331, 1594403, 1595051, 1596509, 4782971, 4782977, 4783697, 14348909 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Clearly, all terms are congruent to 5 modulo 6. By a conjecture in A234337 or A234347, this sequence should have infinitely many terms. Conjecture: For any integer a > 1, there are infinitely many primes of the form a^k + a^m - 1, where k and m are positive integers. LINKS Zhi-Wei Sun, Table of n, a(n) for n = 1..1000 EXAMPLE a(1) = 5 since 3^1 + 3^1 - 1 = 5 is prime. a(2) = 11 since 3^2 + 3^1 - 1 = 11 is prime. MATHEMATICA n=0; Do[If[PrimeQ[3^k+3^m-1], n=n+1; Print[n, " ", 3^k+3^m-1]], {m, 1, 310}, {k, 1, m}] CROSSREFS Cf. A000040, A000079, A000244, A234309, A234310, A234337, A234344, A234347 Sequence in context: A046135 A331946 A162336 * A074267 A268518 A268521 Adjacent sequences:  A234343 A234344 A234345 * A234347 A234348 A234349 KEYWORD nonn AUTHOR Zhi-Wei Sun, Dec 23 2013 STATUS approved

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Last modified April 23 01:20 EDT 2021. Contains 343198 sequences. (Running on oeis4.)