Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #10 Aug 17 2023 20:48:26
%S 10,36,148,676,3237,15876,78685,391876,1955920,9771876,48842100,
%T 244171876,1220773003,6103671876,30517927510,152588671876,
%U 762941200054,3814701171876,19073495062765,95367451171876,476837201876328,2384185888671876,11920929173444139,59604645263671876
%N Maximum number of rational points on a smooth absolutely irreducible projective curve of genus 1 over the field F_5^n.
%H Robin Visser, <a href="/A169880/b169880.txt">Table of n, a(n) for n = 1..1400</a>
%H 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 Gerard van der Geer et al., <a href="http://www.manypoints.org">Tables of curves with many points</a>
%H 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 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 a(n) = 5^n + 1 + floor(2*5^(n/2)) if 5 does not divide floor(2*5^(n/2)), n is even, or n = 1. Otherwise a(n) = 5^n + floor(2*5^(n/2)) [Deuring-Waterhouse]. - _Robin Visser_, Aug 17 2023
%o (Sage)
%o def a(n):
%o if (n==1) or (n%2 == 0) or (floor(2*5^(n/2))%5 != 0):
%o return 5^n + 1 + floor(2*5^(n/2))
%o else:
%o return 5^n + floor(2*5^(n/2)) # _Robin Visser_, Aug 17 2023
%Y Cf. A005523, A169869-A169883.
%K nonn
%O 1,1
%A _N. J. A. Sloane_, Jul 05 2010
%E More terms from _Robin Visser_, Aug 17 2023