A190350 - OEIS

%I #8 Mar 30 2012 16:52:02

%S 1,5,877,3349607,21942759935479332971926241,

%T 180761188752879910424934681877493335110381106645501751786955912877

%N Define a series of lists by L_1 = [1], L_{k+1} = [i+1, i^2+i+1 : i in L_k]; then a(n) = numerator of Sum (1/i : i in L_n).

%C Sum (1/i : i in L_n) converges to Pi/4 as n -> oo.

%D J. Borwein, D. Bailey and R. Girgensohn, Experimentation in Mathematics: Computational Paths to Discovery, Peters, Boston, 2004. See Sect. 1.3.

%e 1, 5/6, 877/1092, 3349607/4218760, 21942759935479332971926241/27765973216255750329906360, ...

%p M:=6; s1:={1}; n1[1]:=1;

%p for n from 2 to M do

%p    s2:={};

%p    for i in s1 do s2:={op(s2), i+1, i^2+i+1 }; od:

%p    n1[n] := add(1/i, i in s2):

%p s1:=s2;

%p od:

%p s3:=[seq(n1[i],i=1..M)];

%Y Cf. A190351.

%K nonn,frac

%O 1,2

%A _N. J. A. Sloane_, May 09 2011