A030125 Decimal expansion of Lehmer's constant.

5, 9, 2, 6, 3, 2, 7, 1, 8, 2, 0, 1, 6, 3, 6, 1, 9, 7, 1, 0, 4, 0, 7, 8, 6, 0, 4, 9, 9, 5, 7, 0, 1, 4, 6, 9, 0, 8, 4, 2, 7, 5, 4, 0, 7, 1, 9, 7, 1, 6, 1, 0, 7, 1, 0, 9, 9, 5, 6, 2, 6, 0, 8, 1, 5, 8, 2, 4, 7, 3, 5, 2, 3, 6, 4, 1, 6, 0, 0, 0, 8, 5, 1, 0, 6, 6, 4, 7, 8, 4, 2, 9, 7, 1, 0, 1, 2, 5, 7, 0, 5, 1, 1, 8

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

Cf. A002065, A002794, A002795, A030125.

Cf. A002665 (continued fraction). - Harry J. Smith, May 14 2009

Sequence in context: A303662 A011494 A214395 * A111698 A216755 A344149

Adjacent sequences: A030122 A030123 A030124 * A030126 A030127 A030128

Keyword

nonn,cons,nice

Author

Eric W. Weisstein

Extensions

More terms from David W. Wilson

Status

approved