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A229919
Denominators of convergents of self-generating continued fraction with first term 2.
2
1, 2, 12, 396, 437580, 533035889100, 791248706534500395281100, 1743421009870075512394843637096042899735399505100
OFFSET
0,2
COMMENTS
For x > 0, define c(x,0) = x and c(x,n) = [c(x,0), ..., c(x,n-1)]. We call f(x) the self-generating continued fraction with first term x. See A229779.
LINKS
EXAMPLE
The first four convergents are 2/1, 5/2, 29/12, 961/396.
MATHEMATICA
z = 10; c[x_, 0] := x; c[x_, n_] := c[x, n] = FromContinuedFraction[Table[c[x, k], {k, 0, n - 1}]]; x = 2; t = Table[c[x, k], {k, 1, z}];
Numerator[t] (* A229918 *)
Denominator[t] (* A229919 *)
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Clark Kimberling, Oct 03 2013
EXTENSIONS
a(7) corrected by Vincenzo Librandi, Oct 13 2013
STATUS
approved