

A055628


Primes p for which the period of the reciprocal 1/p is (p1)/3.


7



103, 127, 139, 331, 349, 421, 457, 463, 607, 661, 673, 691, 739, 829, 967, 1657, 1669, 1699, 1753, 1993, 2011, 2131, 2287, 2647, 2659, 2749, 2953, 3217, 3229, 3583, 3691, 3697, 3739, 3793, 3823, 3931, 4273, 4297, 4513, 4549, 4657, 4903, 4909, 4993, 5011
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OFFSET

1,1


COMMENTS

Cyclic numbers of the third degree (or third order): the reciprocals of these numbers belong to one of three different cycles. Each cycle has (number1)/3 digits.
All primes p except 2 or 5 have a reciprocal with period which divides p1.


REFERENCES

Richards, Stephen P., A NUMBER FOR YOUR THOUGHTS, 1982, 1984, Box 501, New Providence, NJ, 07974, ISBN 0960822402.


LINKS

T. D. Noe, Table of n, a(n) for n=1..1000
Makoto Kamada, Factorizations of 11...11 (Repunit).
Index entries for sequences related to decimal expansion of 1/n


EXAMPLE

127 has period 42 and (1271)/3 = 126/3 = 42


MATHEMATICA

LP[ n_Integer ] := (ds = Divisors[ n  1 ]; Take[ ds, Position[ PowerMod[ 10, ds, n ], 1 ][ [ 1, 1 ] ] ][ [ 1 ] ]); CL[ n_Integer ] := (n  1)/LP[ n ]; Select[ Range[ 7, 7500 ], PrimeQ[ # ] && CL[ # ] == 3 & ]
f[n_Integer] := Block[{ds = Divisors[n  1]}, (n  1)/Take[ ds, Position[ PowerMod[ 10, ds, n], 1] [[1, 1]]] [[ 1]]]; Select[ Prime[ Range[4, 700]], f[ # ] == 3 &] (* Robert G. Wilson v, Sep 14 2004 *)


CROSSREFS

Cf. A054471, A001914, A001913, A097443, A056157, A056210A056217, A098680.
Sequence in context: A095639 A193143 A098049 * A139643 A139957 A077404
Adjacent sequences: A055625 A055626 A055627 * A055629 A055630 A055631


KEYWORD

nonn,base


AUTHOR

Don Willard (dwillard(AT)prairie.cc.il.us), Jun 05 2000


EXTENSIONS

More terms from Robert G. Wilson v, Aug 02 2000
Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, May 27 2007


STATUS

approved



