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

%I A236250 #24 Nov 19 2023 21:15:59
%S A236250 1,6,13,112,51,24,15088,12284,88460,1204,459,31824,93210,1864254,
%T A236250 531648,456036,8299090,28574910,1813560,32552820,33166008,133585180,
%U A236250 2503410,214098720,3183870690,7411133309730,4852769490690,2294509753536,175964053944,3336533898768
%N A236250 Period of the n-th convergent to the continued fraction expansion of Pi.
%F A236250 a(n) = A007732(A002486(n+2)). - _Michel Marcus_, Jan 21 2014
%e A236250 The 2nd convergent is 22/7 = 3.142857 142857 ..., whose period is 6, so a(2) = 6.
%e A236250 The 3rd convergent is 333/106 = 3.1 4150943396226 4150943396226 ..., whose period is 13, so a(3) = 13.
%o A236250 (Sage)
%o A236250 st_clenov = 30
%o A236250 def A236250(n) :
%o A236250    vu = continued_fraction_list(pi, nterms=st_clenov);
%o A236250    p = []
%o A236250    for i in (0..n) :
%o A236250       p.append(convergents(vu)[i].period())
%o A236250    return(p)
%o A236250 A236250(st_clenov-1);
%Y A236250 Cf. A001203, A007732, A084407.
%K A236250 nonn,base
%O A236250 1,2
%A A236250 _Jani Melik_, Jan 21 2014