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 A167389 (arg(exp(-w)) + Im(w)) / (2*Pi), with w = W(n,-log(2)/2)/log(2), where W is the Lambert W function. 5
 2, 3, 5, 6, 8, 9, 10, 12, 13, 15, 16, 18, 19, 21, 22, 23, 25, 26, 28, 29, 31, 32, 34, 35, 36, 38, 39, 41, 42, 44, 45, 47, 48, 49, 51, 52, 54, 55, 57, 58, 60, 61, 62, 64, 65, 67, 68, 70, 71, 72, 74, 75, 77, 78, 80, 81, 83, 84, 85, 87, 88, 90, 91, 93, 94, 96, 97, 98, 100, 101 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The definition seems unnecessarily obscure. What is really going on here? - N. J. A. Sloane, Nov 13 2009 The complement is A172513 with first differences in A172515. - R. J. Mathar, Feb 27 2010 The original definition was: "(argument(exp(-(log(2)+W(n, -log(sqrt(2))))/log(2)))*log(2) + Im(W(n, -log(sqrt(2)))))/(2*Pi*log(2)) where W is the Lambert W function". The expression simplifies to that given in NAME. From the documents in LINKS, it appears that W(n,z) denotes the n-th branch of a complex LambertW function. It remains to understand the intended meaning of the distinction between arg(exp(z)) and Im(z). - M. F. Hasler, Apr 12 2019 LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 Rob Corless, Poster Rob Corless, Lambert W function, copy on web.archove.org as of 07/2011. Stephen Crowley, A Mysterious Three Term Integer Sequence Related to a Lambert W Function Solution to a Certain Transcendental Equation [broken link?] Eric W. Weisstein, MathWorld: Lambert W-Function. Wikipedia, Lambert W function. FORMULA (argument(exp(-(log(2)+W(n,-(1/2)*log(2)))/log(2)))*log(2)+Im(W(n,-(1/2)*log(2))))/ (2*Pi*log(2)) a(n) ~ n/log(2). - Vaclav Kotesovec, Jul 08 2021 MAPLE seq(round(evalf((argument(exp(-(ln(2)+LambertW(n, -(1/2)*ln(2)))/ln(2)))*ln(2)+Im(LambertW(n, -(1/2)*ln(2))))/(2*Pi*ln(2)))), n = 1 .. 100) MATHEMATICA a[n_] := (Arg[Exp[-(Log + ProductLog[n, -1/2*Log])/Log]]* Log + Im[ProductLog[n, -1/2*Log]])/(2*Pi*Log); Table[a[n] // Round, {n, 1, 70}] (* Jean-François Alcover, Jun 20 2013 *) CROSSREFS Cf. A172513 (complement). Sequence in context: A184580 A184622 A195129 * A288373 A087067 A166018 Adjacent sequences:  A167386 A167387 A167388 * A167390 A167391 A167392 KEYWORD nonn,uned AUTHOR Stephen Crowley, Nov 02 2009 STATUS approved

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Last modified September 26 09:30 EDT 2022. Contains 356993 sequences. (Running on oeis4.)