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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
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
KEYWORD
nonn
AUTHOR
A.K. Devaraj, Oct 07 2006
EXTENSIONS
More terms from Don Reble, Oct 07 2006
STATUS
approved