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A005523
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a(n) = maximal number of rational points on an elliptic curve over GF(q), where q = A246655(n) is the n-th prime power > 1.
(Formerly M3757)
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0
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5, 7, 9, 10, 13, 14, 16, 18, 21, 25, 26, 28, 33, 36, 38, 40, 43, 44, 50, 54, 57, 61, 64, 68, 75, 77, 81, 84, 88, 91, 97, 100, 102, 108, 117, 122, 124, 128, 130, 135, 144, 148, 150, 150
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OFFSET
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1,1
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COMMENTS
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The successive values of q are 2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 23, ... (see A246655).
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REFERENCES
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J. W. P. Hirschfeld, Linear codes and algebraic curves, pp. 35-53 of F. C. Holroyd and R. J. Wilson, editors, Geometrical Combinatorics. Pitman, Boston, 1984. See N_q(1) on page 51.
J.-P. Serre, Oeuvres, vol. 3, pp. 658-663 and 664-669.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Table of n, a(n) for n=1..44.
W. C. Waterhouse, Abelian varieties over finite fields, Ann Sci. E.N.S., (4) 2 (1969), 521-560.
Eric Weisstein's World of Mathematics, Rational Point.
Wikipedia, Hasse's theorem on elliptic curves
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FORMULA
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a(n) <= q + 1 + 2*sqrt(q) where q = A246655(n) [Hasse theorem]. - Sean A. Irvine, Jun 26 2020
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EXAMPLE
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a(1) = 5 because 5 is the maximal number of rational points on an elliptic curve over GF(2),
a(2) = 7 because 7 is the maximal number of rational points on an elliptic curve over GF(3),
a(3) = 9 because 9 is the maximal number of rational points on an elliptic curve over GF(4).
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CROSSREFS
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Cf. A000961, A246655.
Sequence in context: A184110 A138892 A190202 * A037084 A018935 A039501
Adjacent sequences: A005520 A005521 A005522 * A005524 A005525 A005526
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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Reworded definition and changed offset so as to clarify the indexing. - N. J. A. Sloane, Jan 08 2017
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STATUS
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approved
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