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 A123239 Primes that do not divide 3^k - 2 for any k. 12
 2, 3, 11, 13, 37, 41, 59, 61, 67, 73, 83, 103, 107, 109, 131, 151, 157, 179, 181, 193, 227, 229, 251, 271, 277, 307, 313, 347, 349, 367, 373, 397, 419, 421, 433, 443, 467, 491, 523, 541, 547, 563, 577, 587, 613, 619, 659, 661, 673, 683, 709, 733, 757, 761 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS That the sequence is infinite can be proved using a theorem in the reference. This sequence contains all primes congruent to 11 or 13 modulo 24, thus is infinite according to Dirichlet's theorem on arithmetic progressions. - Jianing Song, Dec 25 2018 REFERENCES A. K. Devaraj, "Euler's generalization of Fermat's theorem-a further generalization", in ISSN #1550-3747, Proceedings of Hawaii Intl Conference on Statistics, Mathematics & Related Fields, 2004. LINKS Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 MATHEMATICA Select[Prime[Range[135]], !MemberQ[Table[PowerMod[3, k, # ], {k, #-1}], 2]&] (* Farideh Firoozbakht, Oct 11 2006 *) PROG (PARI) is(n)=if(n<4, return(n>1)); if(!isprime(n) || znorder(Mod(3, n)) == n-1, return(0)); my(m=Mod(3, n)); while(m!=1, m*=3; if(m==2, return(0))); 1 \\ Charles R Greathouse IV, Jul 07 2013 CROSSREFS Sequence in context: A235632 A085306 A161322 * A048891 A215358 A191057 Adjacent sequences:  A123236 A123237 A123238 * A123240 A123241 A123242 KEYWORD nonn AUTHOR A.K. Devaraj, Oct 07 2006 EXTENSIONS More terms from Don Reble, Oct 07 2006 STATUS approved

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Last modified May 11 03:49 EDT 2021. Contains 343784 sequences. (Running on oeis4.)