A123239 Primes that do not divide 3^k - 2 for any k.

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

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