OFFSET
1,5
COMMENTS
For more details on Blazys' expansions, see A233582.
Compared with simple continued fraction expansion for sqrt(e), this sequence starts soon growing very rapidly.
LINKS
Stanislav Sykora, Table of n, a(n) for n = 1..1000
S. Sykora, Blazys' Expansions and Continued Fractions, Stans Library, Vol.IV, 2013, DOI 10.3247/sl4math13.001
S. Sykora, PARI/GP scripts for Blazys expansions and fractions, OEIS Wiki
FORMULA
sqrt(e) = 1+1/(1+1/(1+1/(1+1/(5+5/(9+9/(17+17/(109+...))))))).
MATHEMATICA
BlazysExpansion[n_, mx_] := Block[{k = 1, x = n, lmt = mx + 1, s, lst = {}}, While[k < lmt, s = Floor[x]; x = 1/(x/s - 1); AppendTo[lst, s]; k++]; lst]; BlazysExpansion[Sqrt@E, 35] (* Robert G. Wilson v, May 22 2014 *)
PROG
(PARI) bx(x, nmax)={local(c, v, k); // Blazys expansion function
v = vector(nmax); c = x; for(k=1, nmax, v[k] = floor(c); c = v[k]/(c-v[k]); ); return (v); }
bx(exp(1/2), 100) // Execution; use high real precision
CROSSREFS
KEYWORD
nonn
AUTHOR
Stanislav Sykora, Jan 06 2014
STATUS
approved