The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A233584 Coefficients of the generalized continued fraction expansion sqrt(e) = a(1) +a(1)/(a(2) +a(2)/(a(3) +a(3)/(a(4) +a(4)/....))). 11
 1, 1, 1, 1, 5, 9, 17, 109, 260, 2909, 3072, 3310, 3678, 6715, 35175, 37269, 439792, 1400459, 1472451, 4643918, 5683171, 44850176, 62252861, 145631385, 154435765, 371056666, 1685980637, 11196453405, 14795372939 (list; graph; refs; listen; history; text; internal format)
 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 Cf. A019774 (sqrt(e)), A058281 (simple continued fraction). Cf. Blazys' expansions: A233582 (Pi), A233583, A233585, A233586, A233587 and Blazys' continued fractions: A233588, A233589, A233590, A233591. Sequence in context: A334993 A262484 A228956 * A262315 A315119 A061502 Adjacent sequences:  A233581 A233582 A233583 * A233585 A233586 A233587 KEYWORD nonn AUTHOR Stanislav Sykora, Jan 06 2014 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 3 05:36 EDT 2020. Contains 336197 sequences. (Running on oeis4.)