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 A169883 Maximum number of rational points on a smooth absolutely irreducible projective curve of genus 1 over the field F_7^n. 15
 13, 64, 381, 2500, 17066, 118336, 825358, 5769604, 40366312, 282508864, 1977415678, 13841522500, 96889632947, 678224719936, 4747565867723, 33232942099204, 232630544491667, 1628413678617664, 11398895398904361, 79792266862562500, 558545865578002528, 3909821052537641536 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Robin Visser, Table of n, a(n) for n = 1..1000 Max Deuring, Die Typen der Multiplikatorenringe elliptischer Funktionenkörper, Abh. Math. Sem. Hansischen Univ. 14 (1941), 197-272. Gerard van der Geer et al., Tables of curves with many points Gerard van der Geer and Marcel van der Vlugt, Tables of curves with many points, Math. Comp. 69 (2000) 797-810. W. C. Waterhouse, Abelian varieties over finite fields, Ann Sci. E.N.S., (4) 2 (1969), 521-560. FORMULA a(n) = 7^n + 1 + floor(2*7^(n/2)) if 7 does not divide floor(2*7^(n/2)), n is even, or n = 1. Otherwise a(n) = 7^n + floor(2*7^(n/2)) [Deuring-Waterhouse]. - Robin Visser, Aug 17 2023 PROG (Sage) def a(n): if (n==1) or (n%2 == 0) or (floor(2*7^(n/2))%7 != 0): return 7^n + 1 + floor(2*7^(n/2)) else: return 7^n + floor(2*7^(n/2)) # Robin Visser, Aug 17 2023 CROSSREFS Cf. A005523, A169869-A169883. Sequence in context: A067465 A166605 A054477 * A220564 A264513 A302161 Adjacent sequences: A169880 A169881 A169882 * A169884 A169885 A169886 KEYWORD nonn AUTHOR N. J. A. Sloane, Jul 05 2010 EXTENSIONS More terms from Robin Visser, Aug 17 2023 STATUS approved

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Last modified November 30 12:38 EST 2023. Contains 367461 sequences. (Running on oeis4.)