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, 5, 877, 3349607, 21942759935479332971926241, 180761188752879910424934681877493335110381106645501751786955912877

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

Table of n, a(n) for n=1..6.

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

Cf. A190351.

Sequence in context: A214450 A332185 A085706 * A135084 A206356 A298278

Adjacent sequences: A190347 A190348 A190349 * A190351 A190352 A190353

Keyword

nonn,frac

Author

N. J. A. Sloane, May 09 2011

Status

approved