A080702 a(1)=3; for n>1, a(n) = smallest number > a(n-1) such that the condition "if n is in the sequence then a(n) is even" is satisfied.

3, 4, 6, 8, 9, 10, 11, 12, 14, 16, 18, 20, 21, 22, 23, 24, 25, 26, 27, 28, 30, 32, 34, 36, 38, 40, 42, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102

Offset: 1

Author

Benoit Cloitre, Mar 01 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

Crossrefs

Equals A079945(n+1) - 1.

Programs

PARI

lista(nn) = {v = vector(nn); v[1] = 3; prev = v[1]; for (n=2, nn, new = prev+1; if (vecsearch(vecsort(v,,8), n) && (new % 2), new ++); v[n] = new; prev = new;); v;} \\ Michel Marcus, Feb 16 2015

Formula

{a(a(n))} = {2i : i >= 3}.

Extensions

More terms from Matthew Vandermast, Mar 05 2003