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Search: id:A001914
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| A001914 |
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Cyclic numbers: 10 is a quadratic residue modulo p and class of mantissa is 2.
(Formerly M2940 N1183)
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+0
4
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| 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
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Also, 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 (hugo(AT)pfoertner.org), Mar 18 2003
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REFERENCES
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Albert H. Beiler, Recreations in the Theory of Numbers, 2nd ed. New York: Dover, 1966. Pages 65, 309.
M. Kraitchik, Recherches sur la Th\'{e}orie 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).
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EXAMPLE
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The repunit R(6)=111111 is the smallest repunit divisible by the prime a(2)=13=2*6+1.
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CROSSREFS
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Cf. A003277 for another sequence of cyclic numbers.
Cf. A000040, A002275, A071126.
Adjacent sequences: A001911 A001912 A001913 this_sequence A001915 A001916 A001917
Sequence in context: A031414 A030452 A132602 this_sequence A031392 A156980 A158720
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Enoch Haga (Enokh(AT)comcast.net).
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