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

Author

Eric W. Weisstein

Keywords

• nonn
• cons
• nice

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

Examples

			0.592632718201636197104078604995701469084275407197161...
		

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.

Crossrefs

Cf. A002065, A002794, A002795, A030125.

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

Programs

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 *)

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

Formula

Equals cot(Sum_{k>=0} (-1)^k * arccot(A002065(k))). - Amiram Eldar, Aug 18 2020

Extensions

More terms from David W. Wilson