%I #21 May 24 2021 00:57:53

%S 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,

%T 12,12,12,13,14,14,15,14,16,15,16,16,17,18,19,18

%N a(n) is the genus of the modular curve X_0(p) for p = prime(n).

%C 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

%C The previous name was "Genus of Ono X0[p] points". - _Felix Fröhlich_, May 21 2021

%H Ken Ono and Scott Ahlgren, <a href="https://web.archive.org/web/20190304015304/http://www.mathcs.emory.edu/~ono/publications-cv/pdfs/070.pdf">Weierstrass points on X0(p) and supersingular j-invariants</a>, Mathematische Annalen 325 (2003), 355-368, DOI:<a href="https://doi.org/10.1007/s00208-002-0390-9">10.1007/s00208-002-0390-9</a>.

%F From _Felix Fröhlich_, May 21 2021: (Start)

%F a(n) = A001617(prime(n)).

%F Let p = prime(n). Then

%F a(n) = (p-13)/12 if p == 1 (mod 12)

%F a(n) = (p-5)/12 if p == 5 (mod 12)

%F a(n) = (p-7)/12 if p == 7 (mod 12)

%F a(n) = (p+1)/12 if p == 11 (mod 12). (End)

%t g[n_] := (Prime[n] - 13)/12 /; Mod[Prime[n], 12] - 1 == 0

%t g[n_] := (Prime[n] - 5)/12 /; Mod[Prime[n], 12] - 5 == 0

%t g[n_] := (Prime[n] - 7)/12 /; Mod[Prime[n], 12] - 7 == 0

%t g[n_] := (Prime[n] + 1)/12 /; Mod[Prime[n], 12] - 11 == 0

%t Table[g[n], {n, 3, 50}]

%o (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

%Y Cf. A001617.

%K nonn,uned,obsc

%O 3,7

%A _Roger L. Bagula_, Mar 17 2006

%E Offset corrected by _Michel Marcus_, Apr 06 2018

%E Edited by _Felix Fröhlich_, May 21 2021