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A116563 a(n) is the genus of the modular curve X_0(p) for p = prime(n). 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
3,7
COMMENTS
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
LINKS
Ken Ono and Scott Ahlgren, Weierstrass points on X0(p) and supersingular j-invariants, Mathematische Annalen 325 (2003), 355-368, DOI:10.1007/s00208-002-0390-9.
FORMULA
From Felix Fröhlich, May 21 2021: (Start)
a(n) = A001617(prime(n)).
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)
MATHEMATICA
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}]
PROG
(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
CROSSREFS
Cf. A001617.
Sequence in context: A321162 A008668 A225643 * A076695 A071903 A091372
KEYWORD
nonn,uned,obsc
AUTHOR
Roger L. Bagula, Mar 17 2006
EXTENSIONS
Offset corrected by Michel Marcus, Apr 06 2018
Edited by Felix Fröhlich, May 21 2021
STATUS
approved

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Last modified March 29 08:13 EDT 2024. Contains 371265 sequences. (Running on oeis4.)