A080726 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 member of the sequence if and only if a(n) == 2 mod 3".

0, 3, 4, 5, 8, 11, 12, 13, 14, 15, 16, 17, 20, 23, 26, 29, 32, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 56, 59, 62, 65, 68, 71, 74, 77, 80, 83, 86, 89, 92, 95, 98, 101, 104, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119

Offset

0,2

References

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

Links

Table of n, a(n) for n=0..65.

B. Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence, J. Integer Seqs., Vol. 6 (2003), #03.2.2.

B. Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence (math.NT/0305308)

Index entries for sequences of the a(a(n)) = 2n family

Formula

a(a(n)) = 3*n+2, n >= 1.

Prog

(PARI) {a=0; m=[]; for(n=1, 66, print1(a, ", "); a=a+1; if(a%3==2&&a==n, qwqw=qwqw, if(m==[], while((a%3!=2&&a==n)||a%3==2, 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)))}

Crossrefs

Cf. A079000, A080720, ...

Sequence in context: A228305 A103329 A079347 * A101210 A206445 A047599

Adjacent sequences: A080723 A080724 A080725 * A080727 A080728 A080729

Keyword

nonn,easy

Author

N. J. A. Sloane, Mar 08 2003

Extensions

More terms and PARI code from Klaus Brockhaus, Mar 09 2003

Status

approved