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A001914
Cyclic numbers: 10 is a quadratic residue modulo p and class of mantissa is 2.
4
2, 13, 31, 43, 67, 71, 83, 89, 107, 151, 157, 163, 191, 197, 199, 227, 283, 293, 307, 311, 347, 359, 373, 401, 409, 431, 439, 443, 467, 479, 523, 557, 563, 569, 587, 599, 601, 631, 653, 677, 683, 719, 761, 787, 827, 839, 877, 881, 883, 911, 919, 929, 947, 991
OFFSET
1,1
COMMENTS
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
REFERENCES
Albert H. Beiler, Recreations in the Theory of Numbers, 2nd ed. New York: Dover, 1966. Pages 65, 309.
M. Kraitchik, Recherches sur la Théorie des Nombres. Gauthiers-Villars, Paris, Vol. 1, 1924, Vol. 2, 1929, see Vol. 1, p. 61.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
EXAMPLE
The repunit R(6)=111111 is the smallest repunit divisible by the prime a(2)=13=2*6+1.
PROG
(PARI) R(n)=(10^n-1)/9;
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
CROSSREFS
Cf. A003277 for another sequence of cyclic numbers.
Sequence in context: A030452 A132602 A359125 * A254447 A031392 A156980
KEYWORD
nonn
EXTENSIONS
More terms from Enoch Haga
STATUS
approved