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A134474
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a(n) = numerator of Sum_{k=1..n} 1/A134473(k).
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5
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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Table of n, a(n) for n=1..7.
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MAPLE
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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
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MATHEMATICA
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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 *)
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CROSSREFS
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Cf. A134473, A134475, A134476, A134477.
Sequence in context: A054780 A203323 A222683 * A096469 A106423 A077328
Adjacent sequences: A134471 A134472 A134473 * A134475 A134476 A134477
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KEYWORD
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frac,nonn
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AUTHOR
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Leroy Quet, Oct 27 2007
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EXTENSIONS
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More terms from R. J. Mathar, Jul 20 2009
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STATUS
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approved
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