%I A007378 M2317
%S A007378 3,4,6,7,8,10,12,13,14,15,16,18,20,22,24,25,26,27,28,29,30,31,32,34,36,
%T A007378 38,40,42,44,46,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,66,
%U A007378 68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,97,98,99,100,101,102,103
%N A007378 a(n), n>=2, is smallest positive integer which is consistent with sequence 
               being monotonically increasing and satisfying a(a(n)) = 2n.
%C A007378 This is the unique monotonic sequence {a(n)}, n>=2, satisfying a(a(n)) 
               = 2n.
%C A007378 May also be defined by: a(n), n=2,3,4,..., is smallest positive integer 
               greater than a(n-1) which is consistent with the condition "n is 
               a member of the sequence if and only if a(n) is an even number >= 
               4". - N. J. A. Sloane (njas(AT)research.att.com), Feb 23 2003
%C A007378 A monotone sequence satisfying a^(k+1)(n) = mn is unique if m=2, k >= 
               0 or if (k,m) = (1,3). See A088720. - C.L.Mallows (colinm(AT)research.avayalabs.com), 
               Oct 16 2003
%C A007378 Numbers (greater than 2) whose binary representation starts with "11" 
               or ends with "0". - Frank Adams-Watters (FrankTAW(AT)Netscape.net), 
               Jan 17 2006
%D A007378 J.-P. Allouche, N. Rampersad and J. Shallit, On integer sequences whose 
               first iterates are linear, Aequationes Math. 69 (2005), 114-127
%D A007378 J.-P. Allouche and J. Shallit, The ring of k-regular sequences, II, Theoret. 
               Computer Sci., 307 (2003), 3-29.
%D A007378 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A007378 J.-P. Allouche and J. Shallit, <a href="http://www.lri.fr/~allouche/kreg2.ps">
               The Ring of k-regular Sequences, II</a>
%H A007378 B. Cloitre, N. J. A. Sloane and M. J. Vandermast, <a href="http://www.cs.uwaterloo.ca/
               journals/JIS/index.html">Numerical analogues of Aronson's sequence</
               a>, J. Integer Seqs., Vol. 6 (2003), #03.2.2.
%H A007378 B. Cloitre, N. J. A. Sloane and M. J. Vandermast, <a href="http://arXiv.org/
               abs/math.NT/0305308">Numerical analogues of Aronson's sequence</a> 
               (math.NT/0305308)
%H A007378 J. Shallit, <a href="http://www.cs.uwaterloo.ca/~shallit/Talks/kreg7.ps">
               k-regular Sequences</a>
%H A007378 R. Stephan, <a href="somedcgf.html">Some divide-and-conquer sequences 
               ...</a>
%H A007378 R. Stephan, <a href="a079944.ps">Table of generating functions</a>
%H A007378 <a href="Sindx_Aa.html#aan">Index entries for sequences of the a(a(n)) 
               = 2n family</a>
%F A007378 a(2^i + j) = 3*2^(i-1) + j, 0<=j<2^(i-1); a(3*2^(i-1) + j) = 2^(i+1) 
               + 2*j, 0<=j<2^(i-1).
%F A007378 a(3*2^k + j) = 4*2^k + 3j/2 + |j|/2, k>=0, -2^k <= j < 2^k. - N. J. A. 
               Sloane (njas(AT)research.att.com), Feb 23 2003
%F A007378 a(2*n+1) = a(n+1)+a(n), a(2*n) = 2*a(n). a(n) = n+A060973(n). - Vladeta 
               Jovovic (vladeta(AT)eunet.rs), Mar 01 2003
%F A007378 G.f. -x/(1-x) + x/(1-x)^2 * (2 + sum(k>=0, t^2(t-1), t=x^2^k)). - Ralf 
               Stephan (ralf(AT)ark.in-berlin.de), Sep 12 2003
%Y A007378 Cf. A003605. Equals A080653 + 2.
%Y A007378 This sequence, A079905, A080637 and A080653 are all essentially the same.
%Y A007378 Cf. A088720.
%Y A007378 Sequence in context: A022846 A083922 A039042 this_sequence A087758 A105454 
               A127260
%Y A007378 Adjacent sequences: A007375 A007376 A007377 this_sequence A007379 A007380 
               A007381
%K A007378 nonn,easy,nice
%O A007378 2,1
%A A007378 C. L. Mallows (colinm(AT)research.avayalabs.com)
%E A007378 More terms from Matthew Vandermast (ghodges14(AT)comcast.net) and Vladeta 
               Jovovic (vladeta(AT)eunet.rs), Mar 01 2003