%I #15 Nov 26 2017 21:49:57
%S 1,4,5,6,7,10,13,16,17,18,19,20,21,22,23,24,25,28,31,34,37,40,43,46,
%T 49,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,
%U 74,75,76,77,78,79,82,85,88,91,94,97,100,103,106,109,112,115,118,121,124
%N a(0) = 1; for n>0, 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) == 1 mod 3".
%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/VOL6/Cloitre/cloitre2.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 a(a(n)) = 3*n+4, n >= 0.
%o (PARI) {print1(1,","); a=4; m=[4]; for(n=2,68,print1(a,","); a=a+1; if(m[1]==n, while(a%3!=1,a++); m=if(length(m)==1,[],vecextract(m,"2..")),if(a%3==1,a++)); m=concat(m,a))}
%Y Cf. A079000, A080720, ...
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Mar 08 2003
%E More terms and PARI code from _Klaus Brockhaus_, Mar 08 2003