%I A002977 M2335
%S A002977 1,3,4,7,9,10,13,15,19,21,22,27,28,31,39,40,43,45,46,55,57,58,63,64,67,
%T A002977 79,81,82,85,87,91,93,94,111,115,117,118,121,127,129,130,135,136,139,
%U A002977 159,163,165,166,171,172,175,183,187,189,190,193,202,223,231,235,237
%N A002977 a(1) = 1; subsequent terms are defined by the rule that if m is present 
               so are 2m+1 and 3m+1.
%C A002977 Complement of A132142: A132138(a(n)) = 1; for all terms m exists at least 
               one x such that A132140(x)=m. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Aug 20 2007
%D A002977 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A002977 M. L. Fredman and D. E. Knuth, Recurrence relations based on minimization, 
               Abstract 71T-B234, Notices Amer. Math. Soc., 18 (1971), 960.
%D A002977 R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, 
               Reading, MA, 1990, p. 78.
%H A002977 R. Zumkeller, <a href="b002977.txt">Table of n, a(n) for n = 1..10000</
               a>
%H A002977 Benoit Cloitre, <a href="a002977.jpg">Illustration of initial terms</
               a>
%F A002977 It seems that limit as n->infinity of log(A002977(n))/log(n) = C = 1.3.. 
               and probably A002977(n) is asymptotic to u*n^C with u=1.0... - Benoit 
               Cloitre (benoit7848c(AT)orange.fr), Nov 06 2002
%e A002977 a(10)=21=2*(3*(2*1+1)+1)+1: A132139(A132140(10))=A132139(43)=21;
%e A002977 a(14)=31=3*(3*(2*1+1)+1)+1=2*(2*(2*(2*1+1)+1)+1)+1: A132139(A132140(14))=A132139(52)=31 
               and A132139(A132140(16))=A132139(121)=31.
%t A002977 Union[ Flatten[ NestList[{2# + 1, 3# + 1} &, 1, 6]]] (from Robert G. 
               Wilson v (rgwv(AT)rgwv.com), May 11 2005)
%Y A002977 Cf. A007448, A058361, A076291.
%Y A002977 Sequence in context: A032726 A029739 A005098 this_sequence A024799 A039579 
               A115104
%Y A002977 Adjacent sequences: A002974 A002975 A002976 this_sequence A002978 A002979 
               A002980
%K A002977 easy,nonn,nice
%O A002977 1,2
%A A002977 N. J. A. Sloane (njas(AT)research.att.com).
%E A002977 More terms from Ray Chandler (rayjchandler(AT)sbcglobal.net), Sep 06 
               2003