

A141350


Overpseudoprimes of base 3.


4



121, 703, 3281, 8401, 12403, 31621, 44287, 47197, 55969, 74593, 79003, 88573, 97567, 105163, 112141, 211411, 221761, 226801, 228073, 293401, 313447, 320167, 328021, 340033, 359341, 432821, 443713, 453259, 478297, 497503, 504913, 679057, 709873, 801139, 867043, 894781, 973241, 1042417
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OFFSET

1,1


COMMENTS

If h_3(n) is the multiplicative order of 3 modulo n, r_3(n) is the number of cyclotomic cosets of 3 modulo n then, by the definition, n is an overpseudoprime of base 3 if h_3(n)*r_3(n)+1=n. These numbers are in A020229.
In particular, if n is squarefree such that its prime factorization is n=p_1*...*p_k, then n is overpseudoprime of base 3 iff h_3(p_1)=...=h_3(p_k).


REFERENCES

Vladimir Shevelev, Gilberto GarciaPulgarin, Juan Miguel VelasquezSoto and John H. Castillo, Overpseudoprimes, and Mersenne and Fermat numbers as primover numbers, arXiv preprint arXiv:1206:0606, 2012.  From N. J. A. Sloane, Oct 28 2012


LINKS

Table of n, a(n) for n=1..38.
V. Shevelev, Overpseudoprimes, Mersenne Numbers and Wieferich Primes, arXiv:0806.3412v8 [math.NT]


CROSSREFS

Cf. A141232, A137576, A001262, A020229, A062117, A006694.
Sequence in context: A014749 A048950 A020229 * A235408 A190877 A238250
Adjacent sequences: A141347 A141348 A141349 * A141351 A141352 A141353


KEYWORD

nonn


AUTHOR

Vladimir Shevelev, Jun 27 2008, corrected Sep 07 2008


EXTENSIONS

a(10)a(38) from Gilberto GarciaPulgarin  Vladimir Shevelev, Feb 06 2012


STATUS

approved



