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A080596 a(1)=1; for n >= 2, a(n) is smallest positive integer which is consistent with sequence being monotonically increasing and satisfying a(a(n)) = 2n+3.

%I A080596 #8 Nov 26 2017 21:49:57
%S A080596 1,4,5,7,9,10,11,12,13,15,17,19,21,22,23,24,25,26,27,28,29,31,33,35,
%T A080596 37,39,41,43,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,63,65,
%U A080596 67,69,71,73,75,77,79,81,83,85,87,89,91,93,94,95,96,97,98,99,100,101,102
%N A080596 a(1)=1; for n >= 2, a(n) is smallest positive integer which is consistent with sequence being monotonically increasing and satisfying a(a(n)) = 2n+3.
%D A080596 Hsien-Kuei Hwang, S Janson, TH Tsai, Exact and asymptotic solutions of the recurrence f(n) = f(floor(n/2)) + f(ceiling(n/2)) + g(n): theory and applications, Preprint, 2016; http://140.109.74.92/hk/wp-content/files/2016/12/aat-hhrr-1.pdf. Also Exact and Asymptotic Solutions of a Divide-and-Conquer Recurrence Dividing at Half: Theory and Applications, ACM Transactions on Algorithms, 13:4 (2017), #47; DOI: 10.1145/3127585
%H A080596 <a href="/index/Aa#aan">Index entries for sequences of the a(a(n)) = 2n family</a>
%F A080596 a(1) = 1; then a(6*2^k-3+j) = 8*2^k-3+3j/2+|j|/2 for k >= 0, -2^(k+1) <= j < 2^(k+1).
%Y A080596 Cf. A079000. Apart from initial terms, same as A079945.
%K A080596 easy,nonn
%O A080596 1,2
%A A080596 _N. J. A. Sloane_, Feb 23 2003