A080722 - OEIS

%I #25 Jul 15 2022 05:06:32

%S 0,1,3,4,7,8,9,10,13,16,19,20,21,22,23,24,25,26,27,28,31,34,37,40,43,

%T 46,49,52,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,

%U 75,76,77,78,79,80,81,82,85,88,91,94,97,100,103,106,109,112,115,118,121

%N a(0) = 0; 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 term of the sequence if and only if a(n) == 1 (mod 3)".

%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="https://arxiv.org/abs/math/0305308">Numerical analogues of Aronson's sequence</a>, arXiv:math/0305308 [math.NT], 2003.

%H Hsien-Kuei Hwang, Svante Janson, and Tsung-Hsi Tsai, <a href="http://140.109.74.92/hk/wp-content/files/2016/12/aat-hhrr-1.pdf">Exact and asymptotic solutions of the recurrence f(n) = f(floor(n/2)) + f(ceiling(n/2)) + g(n): theory and applications</a>, preprint, 2016.

%H Hsien-Kuei Hwang, Svante Janson, Tsung-Hsi Tsai, <a href="http://doi.org/10.1145/3127585">Exact and Asymptotic Solutions of a Divide-and-Conquer Recurrence Dividing at Half: Theory and Applications</a>, ACM Transactions on Algorithms 13:4 (2017), #47.

%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 >= 2.

%o (PARI) {a=0; m=[]; for(n=1,70,print1(a,","); a=a+1; if(a%3==1&&a==n,qwqw=qwqw,if(m==[], while(a%3!=1&&a==n,a++),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)))} \\ _Klaus Brockhaus_, Mar 08 2003

%Y Cf. A079000, A080720.

%K nonn,easy

%O 0,3

%A _N. J. A. Sloane_, Mar 08 2003

%E More terms from _Klaus Brockhaus_, Mar 08 2003