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A134474 a(n) = numerator of Sum_{k=1..n} 1/A134473(k). 5
1, 3, 32, 5969141, 19747269546873779, 63904014199087613123872206552133781224, 31002867396652810808343087989440323100946378567671674124759425791429267942552085359 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The denominator of Sum_{k=1..n} 1/A134473(k) is A134475(n). A134474(n)/A134475(n) approaches a constant (0.6037789...) as n approaches infinity.

LINKS

Table of n, a(n) for n=1..7.

MAPLE

Digits := 220 ; A134473 := proc(n) option remember ; local su, mu ; if n =1 then 2; else su := add(1/procname(k), k=1..n-1) ; mu := mul(1/(1+1/procname(j)), j=1..n-1) ; ceil( (1+su+sqrt((su-1)^2+4*mu))/2/(mu-su) ) ; fi; end: A134474 := proc(n) add(1/A134473(k), k=1..n) ; numer(%) ; end: seq(A134474(n), n=1..9) ; # R. J. Mathar, Jul 20 2009

MATHEMATICA

b[n_] := b[n] = If[n == 1, 2, With[{x = Product[1/(1 + 1/b[j]), {j, 1, n-1}], y = Sum[1/b[j], {j, 1, n-1}]}, Ceiling[(1 + y + Sqrt[(y-1)^2 + 4 x])/(2 (x-y))]]];

a[n_] := Sum[1/b[k], {k, 1, n}] // Numerator;

Table[a[n], {n, 1, 7}] (* Jean-François Alcover, Sep 26 2022 *)

CROSSREFS

Cf. A134473, A134475, A134476, A134477.

Sequence in context: A054780 A203323 A222683 * A096469 A106423 A077328

Adjacent sequences: A134471 A134472 A134473 * A134475 A134476 A134477

KEYWORD

frac,nonn

AUTHOR

Leroy Quet, Oct 27 2007

EXTENSIONS

More terms from R. J. Mathar, Jul 20 2009

STATUS

approved

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Last modified January 29 13:51 EST 2023. Contains 359923 sequences. (Running on oeis4.)