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 A080727 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) == 2 mod 3". 0

%I

%S 1,2,5,6,7,8,11,14,17,18,19,20,21,22,23,24,25,26,29,32,35,38,41,44,47,

%T 50,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,

%U 75,76,77,78,79,80,83,86,89,92,95,98,101,104,107,110,113,116,119,122

%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) == 2 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+2, n >= 0.

%o (PARI) {a=1; m=[]; for(n=1,69,print1(a,","); a=a+1; if(a%3==2&&a==n,qwqw=qwqw,if(m==[], while(a%3!=2&&a==n,a++),if(m[1]==n, while(a%3!=2,a++); m=if(length(m)==1,[],vecextract(m,"2..")),if(a%3==2,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 09 2003

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Last modified April 20 09:21 EDT 2021. Contains 343125 sequences. (Running on oeis4.)