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 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
 1, 5, 877, 3349607, 21942759935479332971926241, 180761188752879910424934681877493335110381106645501751786955912877 (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. 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

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Last modified December 7 14:54 EST 2023. Contains 367657 sequences. (Running on oeis4.)