A079253 - OEIS

%I #20 Aug 31 2018 09:26:37

%S 0,3,5,6,7,8,10,12,14,15,16,17,18,19,20,22,24,26,28,30,32,33,34,35,36,

%T 37,38,39,40,41,42,43,44,46,48,50,52,54,56,58,60,62,64,66,68,69,70,71,

%U 72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,94,96

%N a(n) is taken to be the 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 even".

%D 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 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 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 <a href="/index/Aa#aan">Index entries for sequences of the a(a(n)) = 2n family</a>

%F For a formula for a(n) see A079000.

%F a(a(n)) = 2n+4 for n >= 1.

%e a(1) cannot be 1 because that would imply that the first term is even; it cannot be 2 because then the first term would be even despite 1's not being in the sequence; therefore a(1)=3, which creates no contradictions and the third term is the first even term of the sequence.

%t a[0] = 0; a[n_] := With[{k = 2^Floor[Log[2, (n+4)/6]]}, (Abs[n - 9k + 4] - 3k + 3n + 6)/2 - 1];

%t Table[a[n], {n, 0, 70}] (* _Jean-François Alcover_, Aug 31 2018 *)

%Y Equals A079000 - 1.

%K nonn

%O 0,2

%A _Matthew Vandermast_ and _N. J. A. Sloane_, Feb 04 2003