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A001914 Cyclic numbers: 10 is a quadratic residue modulo p and class of mantissa is 2.
(Formerly M2940 N1183)
4

%I M2940 N1183

%S 2,13,31,43,67,71,83,89,107,151,157,163,191,197,199,227,283,293,307,

%T 311,347,359,373,401,409,431,439,443,467,479,523,557,563,569,587,599,

%U 601,631,653,677,683,719,761,787,827,839,877,881,883,911,919,929,947,991

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

%C 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 Albert H. Beiler, Recreations in the Theory of Numbers, 2nd ed. New York: Dover, 1966. Pages 65, 309.

%D M. Kraitchik, Recherches sur la Théorie des Nombres. Gauthiers-Villars, Paris, Vol. 1, 1924, Vol. 2, 1929, see Vol. 1, p. 61.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

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

%H Hugo Pfoertner, <a href="/A001914/b001914.txt">Table of n, a(n) for n = 1..1180</a>

%e The repunit R(6)=111111 is the smallest repunit divisible by the prime a(2)=13=2*6+1.

%o (PARI) R(n)=(10^n-1)/9;

%o 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 Cf. A003277 for another sequence of cyclic numbers.

%Y Cf. A000040, A002275, A071126.

%K nonn

%O 1,1

%A _N. J. A. Sloane_

%E More terms from _Enoch Haga_

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Last modified February 15 16:53 EST 2019. Contains 320136 sequences. (Running on oeis4.)