A134475 a(n) = denominator of Sum_{k=1..n} 1/A134473(k).

2, 5, 53, 9886302, 32706124785400851, 105840083750427500921760353826840828183, 51348043200265516352304296553233166994035195487912155511387668758325728717007499617

Offset

1,1

Comments

The numerator of Sum_{k=1..n} 1/A134473(k) is A134474(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: A134475 := proc(n) add(1/A134473(k), k=1..n) ; denom(%) ; end: seq(A134475(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}] // Denominator;
Table[a[n], {n, 1, 7}] (* Jean-François Alcover, Sep 26 2022 *)

Crossrefs

Cf. A134473, A134474, A134476, A134477.

Sequence in context: A071882 A206848 A081482 * A218030 A114029 A013171

Adjacent sequences: A134472 A134473 A134474 * A134476 A134477 A134478

Keyword

frac,nonn

Author

Leroy Quet, Oct 27 2007

Extensions

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

Status

approved