%I A006127 M2547
%S A006127 1,3,6,11,20,37,70,135,264,521,1034,2059,4108,8205,16398,32783,65552,131089,
%T A006127 262162,524307,1048596,2097173,4194326,8388631,16777240,33554457,67108890,
%U A006127 134217755,268435484,536870941,1073741854,2147483679,4294967328,8589934625
%N A006127 2^n + n.
%C A006127 For numbers m=n+2^n such that equation x=2^(m-x) has solution x=2^n, 
               see A103354. - Zak Seidov (zakseidov(AT)yahoo.com), Mar 23 2005
%C A006127 Primes of the form x^x+1 must be of the form 2^2^(a(n))+1, that is, Fermat 
               number F_(a(n)) (Sierpinski 1958). - David W. Wilson (davidwwilson(AT)comcast.net), 
               May 08 2005
%C A006127 a(n) = n-th Mersenne number + n + 1 = A000225(n) + n + 1. Partial sums 
               of a(n) are A132925(n+1), [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), 
               Oct 16 2009]
%D A006127 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A006127 S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques 
               Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%D A006127 John H. Conway, R. K. Guy, The Book of Numbers, Copernicus Press, p. 
               84.
%H A006127 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/MasterThesis.pdf">
               Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures</
               a>, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%H A006127 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/FonctionsGeneratrices.pdf">
               1031 Generating Functions and Conjectures</a>, Universit\'{e} du 
               Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
%H A006127 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=435">
               Encyclopedia of Combinatorial Structures 435</a>
%H A006127 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               SierpinskiNumberoftheFirstKind.html">Sierpinski Number of the First 
               Kind</a>
%F A006127 Row sums of triangle A135227. - Gary W. Adamson (qntmpkt(AT)yahoo.com), 
               Nov 23 2007
%F A006127 Partial sums of A094373. G.f. : (1-x-x^2)/((1-x)^2(1-2x)) - Paul Barry 
               (pbarry(AT)wit.ie), Aug 05 2004
%F A006127 Binomial transform of [1,2,1,1,1,1,1,...]. - Franklin T. Adams-Watters 
               (FrankTAW(AT)Netscape.net), Nov 29 2006
%p A006127 A006127:=(-1+z+z**2)/(2*z-1)/(z-1)**2; [Conjectured by S. Plouffe in 
               his 1992 dissertation.]
%p A006127 g:=1/(1-2*z): gser:=series(g, z=0, 43): seq(coeff(gser, z, n)+n, n=0..34);
               # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 11 2009]
%t A006127 s=3;lst={1, s};Do[s+=(s-n);AppendTo[lst, Abs[s]], {n, 0, 5!}];lst [From 
               Vladimir Orlovsky (4vladimir(AT)gmail.com), Oct 10 2008]
%Y A006127 Cf. A135227.
%Y A006127 Sequence in context: A125896 A094989 A052467 this_sequence A122106 A007707 
               A018174
%Y A006127 Adjacent sequences: A006124 A006125 A006126 this_sequence A006128 A006129 
               A006130
%K A006127 nonn
%O A006127 0,2
%A A006127 N. J. A. Sloane (njas(AT)research.att.com).