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A141390 Overpseudoprimes of base 5. +0
3
781, 5461, 13021, 15751, 25351, 29539, 40501 (list; graph; listen)
OFFSET

1,1

COMMENT

If h_5(n) is the multiplicative order of 5 modulo n, r_5(n) is the number of cyclotomic cosets of 5 modulo n then, by the definition, n is an overpseudoprime of base 5 if h_5(n)*r_5(n)+1=n. These numbers are in A020231.In particular, if n is squarefree such that its prime factorization is

n=p_1*...*p_k, then n is overpseudoprime of base 5 iff h_5(p_1)=...=h_5(p_k).

E.g. since h_5(101)=h_5(251)=h_5(401)=25, then the number 101*251*401=10165751 is in the sequence.

REFERENCES

V. Shevelev, Overpseudoprimes, Mersenne Numbers and Wieferich Primes,arxiv.org /abs/0806.3412

CROSSREFS

Cf. A141232 A141350 A020231 A020229.

Sequence in context: A115467 A020231 A038477 this_sequence A006113 A158398 A003914

Adjacent sequences: A141387 A141388 A141389 this_sequence A141391 A141392 A141393

KEYWORD

nonn

AUTHOR

Vladimir Shevelev (shevelev(AT)bgu.ac.il), Jun 29 2008

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Last modified March 12 18:42 EST 2010. Contains 173425 sequences.


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