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 A030125 Decimal expansion of Lehmer's constant. 6
 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 (list; constant; graph; refs; listen; history; text; internal format)
 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,changed AUTHOR EXTENSIONS More terms from David W. Wilson STATUS approved

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Last modified June 23 18:45 EDT 2021. Contains 345402 sequences. (Running on oeis4.)