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

Author

Jani Melik, Jan 21 2014

Keywords

• nonn
• base

Examples

			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.
		

Crossrefs

Cf. A001203, A007732, A084407.

Programs

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);

Formula

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