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A169883
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Maximum number of rational points on a smooth absolutely irreducible projective curve of genus 1 over the field F_7^n.
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15
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13, 64, 381, 2500, 17066, 118336, 825358, 5769604, 40366312, 282508864, 1977415678, 13841522500, 96889632947, 678224719936, 4747565867723, 33232942099204, 232630544491667, 1628413678617664, 11398895398904361, 79792266862562500, 558545865578002528, 3909821052537641536
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OFFSET
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1,1
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LINKS
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FORMULA
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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
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PROG
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(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:
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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