A006559 Short period primes: the decimal expansion of 1/p has period less than p-1, but greater than zero. (Formerly M2881)

3, 11, 13, 31, 37, 41, 43, 53, 67, 71, 73, 79, 83, 89, 101, 103, 107, 127, 137, 139, 151, 157, 163, 173, 191, 197, 199, 211, 227, 239, 241, 251, 271, 277, 281, 283, 293, 307, 311, 317, 331, 347, 349, 353, 359, 373, 397, 401, 409, 421, 431, 439, 443, 449, 457

Offset

1,1

Comments

Primes 2 and 5 are excluded because 1/2 and 1/5 have no period. Also primes p whose multiplicative order mod p is less than p-1.

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

Victor Meally, Letter to N. J. A. Sloane, no date.

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

Mathematica

Select[Prime[Range[100]], MultiplicativeOrder[10, #] < # - 1 &]

Prog

(PARI) a(n)=gcd(n, 10)==1 && isprime(n) && znorder(Mod(10, n))<n-1 \\ Charles R Greathouse IV, Mar 15 2014

Crossrefs

Cf. A006883.

Sequence in context: A019374 A033680 A032917 * A023248 A199341 A111488

Adjacent sequences: A006556 A006557 A006558 * A006560 A006561 A006562

Keyword

nonn,easy,nice,base

Author

N. J. A. Sloane

Extensions

More terms from James A. Sellers, Aug 21 2000

Status

approved