|
Search: id:A141350
|
|
|
| A141350 |
|
Overpseudoprimes of base 3. |
|
+0
5
|
|
| 121, 703, 3281, 8401, 12403, 31621, 44287, 47197, 55969
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
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
|
V. Shevelev, Overpseudoprimes, Mersenne Numbers and Wieferich Primes, arxiv.org/abs/0806.3412
|
|
CROSSREFS
|
Cf. A141232 A137576 A001262 A020229 A062117 A006694.
Adjacent sequences: A141347 A141348 A141349 this_sequence A141351 A141352 A141353
Sequence in context: A014749 A048950 A020229 this_sequence A120353 A036928 A088171
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Vladimir Shevelev (shevelev(AT)bgu.ac.il), Jun 27 2008, corrected Sep 07 2008
|
|
|
Search completed in 0.002 seconds
|
