A236250 Period of the n-th convergent to the continued fraction expansion of Pi.

1, 6, 13, 112, 51, 24, 15088, 12284, 88460, 1204, 459, 31824, 93210, 1864254, 531648, 456036, 8299090, 28574910, 1813560, 32552820, 33166008, 133585180, 2503410, 214098720, 3183870690, 7411133309730, 4852769490690, 2294509753536, 175964053944, 3336533898768

Offset

1,2

Links

Table of n, a(n) for n=1..30.

Formula

a(n) = A007732(A002486(n+2)). - Michel Marcus, Jan 21 2014

Example

The 2nd convergent is 22/7 = 3.142857 142857 ..., whose period is 6, so a(2) = 6.
The 3rd convergent is 333/106 = 3.1 4150943396226 4150943396226 ..., whose period is 13, so a(3) = 13.

Prog

(Sage)
st_clenov = 30
def A236250(n) :
   vu = continued_fraction_list(pi, nterms=st_clenov);
   p = []
   for i in (0..n) :
      p.append(convergents(vu)[i].period())
   return(p)
A236250(st_clenov-1);

Crossrefs

Cf. A001203, A007732, A084407.

Sequence in context: A042641 A292121 A364199 * A336046 A368633 A042285

Adjacent sequences: A236247 A236248 A236249 * A236251 A236252 A236253

Keyword

nonn,base

Author

Jani Melik, Jan 21 2014

Status

approved