cp's OEIS Frontend

A169883 Maximum number of rational points on a smooth absolutely irreducible projective curve of genus 1 over the field F_7^n.

%I A169883 #10 Aug 17 2023 20:43:43
%S A169883 13,64,381,2500,17066,118336,825358,5769604,40366312,282508864,
%T A169883 1977415678,13841522500,96889632947,678224719936,4747565867723,
%U A169883 33232942099204,232630544491667,1628413678617664,11398895398904361,79792266862562500,558545865578002528,3909821052537641536
%N A169883 Maximum number of rational points on a smooth absolutely irreducible projective curve of genus 1 over the field F_7^n.
%H A169883 Robin Visser, <a href="/A169883/b169883.txt">Table of n, a(n) for n = 1..1000</a>
%H A169883 Max Deuring, <a href="https://doi.org/10.1007/BF02940746">Die Typen der Multiplikatorenringe elliptischer Funktionenkörper</a>, Abh. Math. Sem. Hansischen Univ. 14 (1941), 197-272.
%H A169883 Gerard van der Geer et al., <a href="http://www.manypoints.org">Tables of curves with many points</a>
%H A169883 Gerard van der Geer and Marcel van der Vlugt, <a href="https://doi.org/10.1090/S0025-5718-99-01143-6">Tables of curves with many points</a>, Math. Comp. 69 (2000) 797-810.
%H A169883 W. C. Waterhouse, <a href="https://doi.org/10.24033/asens.1183">Abelian varieties over finite fields</a>, Ann Sci. E.N.S., (4) 2 (1969), 521-560.
%F A169883 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
%o A169883 (Sage)
%o A169883 def a(n):
%o A169883     if (n==1) or (n%2 == 0) or (floor(2*7^(n/2))%7 != 0):
%o A169883         return 7^n + 1 + floor(2*7^(n/2))
%o A169883     else:
%o A169883         return 7^n + floor(2*7^(n/2))  # _Robin Visser_, Aug 17 2023
%Y A169883 Cf. A005523, A169869-A169883.
%K A169883 nonn
%O A169883 1,1
%A A169883 _N. J. A. Sloane_, Jul 05 2010
%E A169883 More terms from _Robin Visser_, Aug 17 2023