

A190350


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).


1




OFFSET

1,2


COMMENTS

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


REFERENCES

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


LINKS



EXAMPLE

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


MAPLE

M:=6; s1:={1}; n1[1]:=1;
for n from 2 to M do
s2:={};
for i in s1 do s2:={op(s2), i+1, i^2+i+1 }; od:
n1[n] := add(1/i, i in s2):
s1:=s2;
od:
s3:=[seq(n1[i], i=1..M)];


CROSSREFS



KEYWORD

nonn,frac


AUTHOR



STATUS

approved



