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".

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, 50, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 83, 86, 89, 92, 95, 98, 101, 104, 107, 110, 113, 116, 119, 122

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..67.

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 >= 0.

Prog

(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)))}

Crossrefs

Cf. A079000, A080720, ...

Sequence in context: A074940 A028752 A028791 * A283974 A028739 A074291

Adjacent sequences: A080724 A080725 A080726 * A080728 A080729 A080730

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