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

Author

N. J. A. Sloane, Mar 08 2003

Keywords

• nonn
• easy

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

• 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

Crossrefs

Cf. A079000, A080720, ...

Programs

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)))}

Formula

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

Extensions

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