A002667 Continued cotangent for Pi.

3, 73, 8599, 400091364, 371853741549033970, 253461181173408820488703379557217678

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

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 = 0..9
• D. H. Lehmer, A cotangent analogue of continued fractions, Duke Math. J., 4 (1935), 323-340. [Annotated scanned copy]
• Index entries for sequences related to the number Pi

Programs

Mathematica

Floor[NestList[(#*Floor[#]+1)/(#-Floor[#]) &, Pi, 5]] (* Stefano Spezia, Apr 24 2025 *)

PARI

{ default(realprecision, 10000); bn=vector(10); bn[1]=Pi; for(n=2, 10, bn[n]=(bn[n-1]*floor(bn[n-1]) + 1)/(bn[n-1] - floor(bn[n-1]))); for (n=1, 10, write("b002667.txt", n-1, " ", floor(bn[n]))); } \\ Harry J. Smith, May 04 2009

Extensions

More terms from Jeffrey Shallit