A006559 - OEIS

%I M2881 #33 Dec 18 2021 20:52:46

%S 3,11,13,31,37,41,43,53,67,71,73,79,83,89,101,103,107,127,137,139,151,

%T 157,163,173,191,197,199,211,227,239,241,251,271,277,281,283,293,307,

%U 311,317,331,347,349,353,359,373,397,401,409,421,431,439,443,449,457

%N Short period primes: the decimal expansion of 1/p has period less than p-1, but greater than zero.

%C 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.

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

%H T. D. Noe, <a href="/A006559/b006559.txt">Table of n, a(n) for n = 1..1000</a>

%H Victor Meally, <a href="/A006556/a006556.pdf">Letter to N. J. A. Sloane</a>, no date.

%H <a href="/index/1#1overn">Index entries for sequences related to decimal expansion of 1/n</a>

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

%o (PARI) a(n)=gcd(n,10)==1 && isprime(n) && znorder(Mod(10,n))<n-1 \\ _Charles R Greathouse IV_, Mar 15 2014

%Y Cf. A006883.

%K nonn,easy,nice,base

%O 1,1

%A _N. J. A. Sloane_

%E More terms from _James A. Sellers_, Aug 21 2000