OFFSET
1,1
REFERENCES
D. H. Lehmer, A cotangent analogue of continued fractions, Duke Math. J., 4 (1935), 323-340.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Harry J. Smith, Table of n, a(n) for n = 1..11
D. H. Lehmer, A cotangent analogue of continued fractions, Duke Math. J., 4 (1935), 323-340. [Annotated scanned copy]
Eric Weisstein's World of Mathematics, Lehmer Cotangent Expansion
MATHEMATICA
b[1] = E; b[n_] := b[n] = (b[n-1]*Floor[b[n-1]]+1) / (b[n-1]-Floor[b[n-1]]); a[n_] := Floor[b[n]]; Table[a[n], {n, 1, 8}] (* Jean-François Alcover, Jan 17 2012, after PARI *)
PROG
(PARI) { default(realprecision, 10000); bn=vector(11); bn[1]=exp(1); for(n=2, 11, bn[n]=(bn[n-1]*floor(bn[n-1]) + 1)/(bn[n-1] - floor(bn[n-1]))); for (n=1, 11, write("b002668.txt", n, " ", floor(bn[n]))); } \\ Harry J. Smith, May 04 2009
CROSSREFS
KEYWORD
nonn,easy,nice
AUTHOR
EXTENSIONS
More terms from Jeffrey Shallit
STATUS
approved