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