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A190351 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) = denominator of Sum (1/i : i in L_n). 1
1, 6, 1092, 4218760, 27765973216255750329906360, 229254309739144896253372216696442967123093789661296276592384463520 (list; graph; refs; listen; history; text; internal format)
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. A190350.

Sequence in context: A003763 A179853 A268043 * A267071 A219165 A185537

Adjacent sequences:  A190348 A190349 A190350 * A190352 A190353 A190354

KEYWORD

nonn,frac

AUTHOR

N. J. A. Sloane, May 09 2011

STATUS

approved

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Last modified May 27 16:48 EDT 2022. Contains 354110 sequences. (Running on oeis4.)