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A045616 Primes p such that the decimal fraction 1/p has same period length as 1/p^2. 4
3, 487, 56598313 (list; graph; refs; listen; history; internal format)
OFFSET

1,1

COMMENTS

56598313 was announced in the paper by Brillhart et al. No further terms up to 2*10^11 - Helmut Richter (richter(AT)lrz.de), May 17 2004

REFERENCES

J. Brillhart, J. Tonascia, and P. Weinberger, On the Fermat quotient, pp. 213-222 of A. O. L. Atkin and B. J. Birch, editors, Computers in Number Theory. Academic Press, NY, 1971.

Richard K. Guy, Unsolved Problems in Number Theory, Springer, 2004, A3.

Peter L. Montgomery, New Solutions of a^(p-1) = 1 (mod p^2), Math. Comp. 61 (1993), 361-363.

Samuel Yates, The Mystique of Repunits, Math. Mag. 51 (1978), 22-28.

LINKS

Helmut Richter, The period length of the decimal expansion of a fraction

Helmut Richter, The Prime Factors Of 10^486-1

FORMULA

Primes p such that 10^(p-1) == 1 (mod p^2)

CROSSREFS

Analogous sequence for base 2 instead of 10 (Wieferich primes): A001220. First members of analogous sequences for all bases: A039951.

Sequence in context: A140015 A203681 A195611 * A198705 A198624 A198652

Adjacent sequences:  A045613 A045614 A045615 * A045617 A045618 A045619

KEYWORD

bref,hard,nonn,nice,more,base

AUTHOR

Helmut Richter (richter(AT)lrz.de)

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Last modified February 10 12:50 EST 2012. Contains 205246 sequences.