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A005523 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)
0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The successive values of q are 2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 23, ... (see A246655).

REFERENCES

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).

LINKS

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

FORMULA

a(n) <= q + 1 + 2*sqrt(q) where q = A246655(n) [Hasse theorem]. - Sean A. Irvine, Jun 26 2020

EXAMPLE

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).

CROSSREFS

Cf. A000961, A246655.

Sequence in context: A184110 A138892 A190202 * A037084 A018935 A039501

Adjacent sequences:  A005520 A005521 A005522 * A005524 A005525 A005526

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Reworded definition and changed offset so as to clarify the indexing. - N. J. A. Sloane, Jan 08 2017

STATUS

approved

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Last modified June 13 11:36 EDT 2021. Contains 344990 sequences. (Running on oeis4.)