OFFSET
0,1
COMMENTS
Digits 999 and 1000 should be "48" not "65" as given in the Plouffe links. - Sean A. Irvine, Aug 24 2014
Named after the American mathematician Derrick Henry Lehmer (1905-1991). - Amiram Eldar, Jun 22 2021
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 433-434.
LINKS
Simon Plouffe and Sean A. Irvine, Table of n, a(n) for n = 0..2000 [Replaces terms 0..998 from Harry J. Smith.]
Steven R. Finch, Lehmer's Constant. [Broken link]
Steven R. Finch, Lehmer's Constant. [From the Wayback machine]
D. H. Lehmer, A cotangent analogue of continued fractions, Duke Math. J., Vol. 4, No. 2 (1938), pp. 323-340. [Annotated scanned copy]
Simon Plouffe, The Lehmer Constant to 1000 digits.
Simon Plouffe, The Lehmer constant to 1000 digits.
Eric Weisstein's World of Mathematics, Lehmer's Constant.
FORMULA
Equals cot(Sum_{k>=0} (-1)^k * arccot(A002065(k))). - Amiram Eldar, Aug 18 2020
EXAMPLE
0.592632718201636197104078604995701469084275407197161...
MATHEMATICA
RealDigits[With[{nn=15}, Cot[Total[Last[#]ArcCot[First[#]]&/@Thread[ {NestList[ #^2+#+1&, 0, nn], PadRight[{}, nn+1, {1, -1}]}]]]], 10, 120][[1]] (* Harvey P. Dale, Jan 29 2012 *)
PROG
(PARI) b=0.; 1/tan(suminf(k=1, b=b^2+b+1; (-1)^k*atan(1/b))+Pi/2) \\ Charles R Greathouse IV, Jan 21 2016
CROSSREFS
KEYWORD
AUTHOR
EXTENSIONS
More terms from David W. Wilson
STATUS
approved