

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 nth 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 WFunction.
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[2] + ProductLog[n, 1/2*Log[2]])/Log[2]]]* Log[2] + Im[ProductLog[n, 1/2*Log[2]]])/(2*Pi*Log[2]); Table[a[n] // Round, {n, 1, 70}] (* JeanFrançois 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



