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A001914 Cyclic numbers: 10 is a quadratic residue modulo p and class of mantissa is 2.

%I A001914 M2940 N1183 #23 Sep 18 2018 04:48:33
%S A001914 2,13,31,43,67,71,83,89,107,151,157,163,191,197,199,227,283,293,307,
%T A001914 311,347,359,373,401,409,431,439,443,467,479,523,557,563,569,587,599,
%U A001914 601,631,653,677,683,719,761,787,827,839,877,881,883,911,919,929,947,991
%N A001914 Cyclic numbers: 10 is a quadratic residue modulo p and class of mantissa is 2.
%C A001914 Also, apart from first term 2, primes p for which the repunit (A002275) R((p-1)/2)=(10^((p-1)/2)-1)/9 is the smallest repunit divisible by p. Primes for which A000040(n) = 2*A071126(n) + 1. - _Hugo Pfoertner_, Mar 18 2003, Sep 18 2018
%D A001914 Albert H. Beiler, Recreations in the Theory of Numbers, 2nd ed. New York: Dover, 1966. Pages 65, 309.
%D A001914 M. Kraitchik, Recherches sur la Théorie des Nombres. Gauthiers-Villars, Paris, Vol. 1, 1924, Vol. 2, 1929, see Vol. 1, p. 61.
%D A001914 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A001914 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A001914 Hugo Pfoertner, <a href="/A001914/b001914.txt">Table of n, a(n) for n = 1..1180</a>
%e A001914 The repunit R(6)=111111 is the smallest repunit divisible by the prime a(2)=13=2*6+1.
%o A001914 (PARI) R(n)=(10^n-1)/9;
%o A001914 print1(2,", "); forprime(p=3, 1000, m=0; for(q=3, (p-1)/2-1, if(R(q)%p==0, m=1; break));if(m==0&&R((p-1)/2)%p==0, print1(p,", "))) \\ _Hugo Pfoertner_, Sep 18 2018
%Y A001914 Cf. A003277 for another sequence of cyclic numbers.
%Y A001914 Cf. A000040, A002275, A071126.
%K A001914 nonn
%O A001914 1,1
%A A001914 _N. J. A. Sloane_
%E A001914 More terms from _Enoch Haga_