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A116563
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a(n) is the genus of the modular curve X_0(p) for p = prime(n).
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2
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0, 0, 1, 0, 1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 5, 4, 5, 6, 5, 6, 7, 7, 7, 8, 8, 9, 8, 9, 10, 11, 11, 11, 12, 12, 12, 13, 14, 14, 15, 14, 16, 15, 16, 16, 17, 18, 19, 18
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OFFSET
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3,7
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COMMENTS
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Also the dimension of the space of cusp forms of weight two and level p, where p=5, 7, 11, 13, ... ranges over all primes exceeding 3. - Steven Finch, Apr 04 2007
The previous name was "Genus of Ono X0[p] points". - Felix Fröhlich, May 21 2021
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LINKS
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FORMULA
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Let p = prime(n). Then
a(n) = (p-13)/12 if p == 1 (mod 12)
a(n) = (p-5)/12 if p == 5 (mod 12)
a(n) = (p-7)/12 if p == 7 (mod 12)
a(n) = (p+1)/12 if p == 11 (mod 12). (End)
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MATHEMATICA
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g[n_] := (Prime[n] - 13)/12 /; Mod[Prime[n], 12] - 1 == 0
g[n_] := (Prime[n] - 5)/12 /; Mod[Prime[n], 12] - 5 == 0
g[n_] := (Prime[n] - 7)/12 /; Mod[Prime[n], 12] - 7 == 0
g[n_] := (Prime[n] + 1)/12 /; Mod[Prime[n], 12] - 11 == 0
Table[g[n], {n, 3, 50}]
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PROG
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(PARI) a(n) = {my(p = prime(n), m = p % 12); if (m==1, (p-13)/12, if (m==5, (p-5)/12, if (m==7, (p-7)/12, if (m==11, (p+1)/12)))); } \\ Michel Marcus, Apr 06 2018
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CROSSREFS
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KEYWORD
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nonn,uned,obsc
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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