OFFSET
1,1
COMMENTS
LINKS
Andrew N. W. Hone, Curious continued fractions, nonlinear recurrences and transcendental numbers, arXiv:1507.00063 [math.NT], 2015 and J. Int. Seq. 18 (2015) # 15.8.4.
EXAMPLE
2.584401724019776724812076147153331342112382090467969...
= Sum_{n>=0} 1/A112373(n) = 1/1 +1/1 +1/2 +1/12 +1/936 +1/68408496 +...
= [2;1,1,2,2,6,12,78,936,73086,68408496,...] (continued fraction).
MATHEMATICA
dm = 5; digits = 105;
b[n_] := b[n] = If[n < 2, 1, (b[n - 1]^3 + b[n - 1]^2)/b[n - 2]];
s[m_] := s[m] = N[Sum[1/b[n], {n, 0, m}], digits + 5];
s[m = dm];
s[m += dm];
While[RealDigits[s[m]] != RealDigits[s[m - dm]], m += dm];
RealDigits[s[m], 10, digits][[1]] (* Jean-François Alcover, Sep 30 2019 *)
c[0]=2; c[1] = c[2] = 1; c[n_] := c[n] = c[n-1] c[n-2] + Mod[n, 2] c[n-2];
RealDigits[FromContinuedFraction[c /@ Range[0, 14]], 10, 105][[1]] (* Jean-François Alcover, Oct 01 2019 *)
CROSSREFS
KEYWORD
cons,nonn
AUTHOR
Paul D. Hanna, Dec 08 2005
STATUS
approved