A054471 Smallest prime p having n different cycles in decimal expansions of k/p, k=1..p-1.

7, 3, 103, 53, 11, 79, 211, 41, 73, 281, 353, 37, 2393, 449, 3061, 1889, 137, 2467, 16189, 641, 3109, 4973, 11087, 1321, 101, 7151, 7669, 757, 38629, 1231, 49663, 12289, 859, 239, 27581, 9613, 18131, 13757, 33931, 9161, 118901, 6763, 18233

Offset

1,1

Comments

First cyclic number of n-th degree (or n-th order): the reciprocals of these numbers belong to one of n different cycles. Each cycle has (a(n) - 1)/n digits.

From Robert G. Wilson v, Aug 21 2014: (Start)

recursive by indices:

1, 7, 211, 79337, 634776923741, ...

2, 3, 103, 2368589, 785245568161181, ...

4, 53, 135257, 2332901103899, ...

5, 11, 353, 3795457, 693814982285339, ...

6, 79, 26861, 23947548497, ...

8, 41, 118901, 1015118238709, ...

9, 73, 142789, 267291583927, ...

10, 281, 3097183, 66880786504811, ...

12, 37, 18131, 105385168331, ...

13, 2393, 11160953, ...

... .

(End)

References

John H. Conway and R. K. Guy, The Book of Numbers, Copernicus Press, p. 162.

M. Gardner, Mathematical Circus, Cambridge University Press (1996).

Links

Robert G. Wilson v, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)

H. Richter, The period length of the decimal expansion of a fraction

Index entries for sequences related to decimal expansion of 1/n

Mathematica

f[n_Integer] := Block[{k = 1, p}, While[p = k*n + 1; ! PrimeQ[p] || p != 1 + n*MultiplicativeOrder[10, p] || GCD[10, p] > 1, k++]; p]; Array[f, 50] (* Robert G. Wilson v, Apr 19 2005; revised Aug 20 2014 *)

Crossrefs

First time n appears in A006556.

Cf. A006883, A097443, A055628, A056157, A056210, A056211, A056212, A056213, A056214, A056215, A056216, A056217, A098680, which are sequences of primes p where the period of the reciprocal is (p-1)/n for n=1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13.

Cf. A101208, A101209 (similar sequences for base 2 and base 3).

Sequence in context: A173443 A003723 A241438 * A086453 A320842 A112099

Adjacent sequences: A054468 A054469 A054470 * A054472 A054473 A054474

Keyword

nonn,easy,nice,base

Author

Robert G. Wilson v, 1994; Antreas P. Hatzipolakis (xpolakis(AT)otenet.gr), May 22 2000

Extensions

More terms from David W. Wilson, May 22 2000

Status

approved