cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A030798 Decimal expansion of the solution to x^x = 2.

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%I A030798 #56 Feb 13 2024 12:44:36
%S A030798 1,5,5,9,6,1,0,4,6,9,4,6,2,3,6,9,3,4,9,9,7,0,3,8,8,7,6,8,7,6,5,0,0,2,
%T A030798 9,9,3,2,8,4,8,8,3,5,1,1,8,4,3,0,9,1,4,2,4,7,1,9,5,9,4,5,6,9,4,1,3,9,
%U A030798 7,3,0,3,4,5,4,9,5,9,0,5,8,7,1,0,5,4,1,3,4,4,4,6,9,1,2,8,3,9,7,3,6
%N A030798 Decimal expansion of the solution to x^x = 2.
%C A030798 The constant 1.559610469462... is transcendental. - Nick Hobson, Nov 29 2006
%H A030798 G. C. Greubel, <a href="/A030798/b030798.txt">Table of n, a(n) for n = 1..10000</a>
%H A030798 Nick Hobson, <a href="https://web.archive.org/web/20160414002427/http://www.qbyte.org/puzzles/p029s.html#remark">Solution to puzzle 29: x^x. Remark: x^x = 2</a>.
%H A030798 Gianni Sarcone, <a href="http://www.archimedes-lab.org/numbers/Num1_69.html">Zoo of Numbers: Numbers NaN to 6</a>, Archimedes Lab, Genoa, Italy.
%H A030798 Jonathan Sondow and Diego Marques, <a href="http://arxiv.org/abs/1108.6096">Algebraic and transcendental solutions of some exponential equations</a>, arXiv:1108.6096 [math.NT], 2011; Annales Mathematicae et Informaticae 37 (2010) 151-164; see top of p. 4 in the link.
%H A030798 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F A030798 Equals log(2)/LambertW(log(2)). - _Simon Plouffe_, Mar 23 2005
%F A030798 Equals 1/A104748.
%e A030798 1.559610469462369349970388768765002993284883511843091424719594569...
%t A030798 RealDigits[ Log[2]/ProductLog[Log[2]], 10, 111][[1]] (* _Robert G. Wilson v_, Mar 23 2005 *)
%t A030798 RealDigits[x/.FindRoot[x^x==2,{x,1},WorkingPrecision->120]][[1]] (* _Harvey P. Dale_, May 27 2020 *)
%o A030798 (PARI) solve(x=1, 2, x^x-2) \\ _Michel Marcus_, Jan 14 2015
%o A030798 (PARI) log(2)/lambertw(log(2)) \\ _Charles R Greathouse IV_, May 14 2019
%Y A030798 Cf. A153510 (continued fraction), A199550 (x^x^x = 2).
%K A030798 nonn,cons
%O A030798 1,2
%A A030798 _N. J. A. Sloane_, _Simon Plouffe_
%E A030798 Definition clarified by _Jonathan Sondow_, Sep 02 2011