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A006559 Short period primes: the decimal expansion of 1/p has period less than p-1, but greater than zero.
(Formerly M2881)
3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 15 00:30 EST 2019. Contains 329988 sequences. (Running on oeis4.)