A002666 Continued cotangent for square root of 2. (Formerly M3983 N1652)

1, 5, 36, 3406, 14694817, 727050997716715, 2074744506784679417243551677046, 46045625970633183674340934067371917846908361831894602280765110

Offset

0,2

References

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 = 0..11

D. H. Lehmer, A cotangent analogue of continued fractions, Duke Math. J., 4 (1935), 323-340. [Annotated scanned copy]

D. H. Lehmer, A cotangent analogue of continued fractions, Duke Math. J., 4 (1935), 323-340.

Eric Weisstein's World of Mathematics, Lehmer Cotangent Expansion.

Mathematica

Floor[NestList[(#*Floor[#]+1)/(#-Floor[#]) &, Sqrt[2], 7]] (* Stefano Spezia, Apr 24 2025 *)

Prog

(PARI) { default(realprecision, 10000); bn=vector(12); bn[1]=sqrt(2); for(n=2, 12, bn[n]=(bn[n-1]*floor(bn[n-1]) + 1)/(bn[n-1] - floor(bn[n-1]))); for (n=1, 12, print1(floor(bn[n]), ", ")); } \\ Harry J. Smith, May 04 2009

Crossrefs

Sequence in context: A118018 A318424 A156355 * A222592 A174507 A119483

Adjacent sequences: A002663 A002664 A002665 * A002667 A002668 A002669

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Jeffrey Shallit

Status

approved