Search: id:A030124
Results 1-1 of 1 results found.

%I A030124
%S A030124 2,4,5,6,8,9,10,11,13,14,15,16,17,19,20,21,22,23,24,25,27,28,29,30,
%T A030124 31,32,33,34,36,37,38,39,40,41,42,43,44,46,47,48,49,50,51,52,53,54,
%U A030124 55,57,58,59,60,61,62,63,64,65,66,67,68,70,71,72,73,74,75,76,77,78
%N A030124 Complement (and also first differences) of Hofstadter's sequence A005228.
%C A030124 For any n, all integers k satisfying sum(i=1,n,a(i))+1<k<sum(i=1,n+1,
               a(i))+1 are in the sequence. E.g. sum(i=1,3,a(i))+1=12, sum(i=1,4,
               a(i))+1=18, hence 13,14,15,16,17 are in the sequence. - Benoit Cloitre 
               (benoit7848c(AT)orange.fr), Apr 01 2002
%C A030124 The asymptotic equivalence a(n) ~ n follows from the fact that the values 
               disallowed in the present sequence because they occur in A005228 
               are negligible, since A005228 grows much faster than A030124. The 
               next-to-leading term in the formula is calculated from the functional 
               equation F(x) + G(x) = x, suggested by D. Wilson (cf. reference), 
               where F and G are the inverse functions of smooth, increasing approximations 
               f and f' of A005228 and A030124. It seems that higher order corrections 
               calculated from this equation do not agree with the real behaviour 
               of a(n). - M. F. Hasler (www.univ-ag.fr/~mhasler), Jun 04 2008
%D A030124 E. Angelini, "Jeux de suites", in Dossier Pour La Science, pp. 32-35, 
               Volume 59 (Jeux math'), April/June 2008, Paris.
%D A030124 Hofstadter, "Goedel, Escher, Bach", p. 73.
%D A030124 D. W. Wilson, "Asymptotics about A005228", Posting Jun 03 2008 on SeqFan 
               mailing list (www.seqfan.eu).
%H A030124 T. D. Noe, <a href="b030124.txt">Table of n, a(n) for n=0..1000</a>
%H A030124 N. J. A. Sloane, <a href="http://www.research.att.com/~njas/doc/sg.txt">
               My favorite integer sequences</a>, in Sequences and their Applications 
               (Proceedings of SETA '98).
%H A030124 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               HofstadterFigure-FigureSequence.html">Link to a section of The World 
               of Mathematics.</a>
%H A030124 <a href="Sindx_Go.html#GEB">Index entries for sequences from "Goedel, 
               Escher, Bach"</a>
%F A030124 A030124(n) = n + sqrt(2n) + o(n^(1/2)) - M. F. Hasler (www.univ-ag.fr/
               ~mhasler), Jun 04 2008
%o A030124 (PARI) a=b=t=1;for(i=1,100, while(bittest(t,b++),);print1(b",");t+=1<<b+1<<a+=b) 
               - M. F. Hasler (www.univ-ag.fr/~mhasler), Jun 04 2008
%Y A030124 Sequence in context: A080240 A135668 A039138 this_sequence A064318 A039100 
               A141204
%Y A030124 Adjacent sequences: A030121 A030122 A030123 this_sequence A030125 A030126 
               A030127
%K A030124 nonn
%O A030124 0,1
%A A030124 Eric Weisstein (eric(AT)weisstein.com)

Search completed in 0.002 seconds