A079253 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) is even".

0, 3, 5, 6, 7, 8, 10, 12, 14, 15, 16, 17, 18, 19, 20, 22, 24, 26, 28, 30, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 94, 96

Offset: 0

Author

Matthew Vandermast and N. J. A. Sloane, Feb 04 2003

Keywords

• nonn

Examples

			a(1) cannot be 1 because that would imply that the first term is even; it cannot be 2 because then the first term would be even despite 1's not being in the sequence; therefore a(1)=3, which creates no contradictions and the third term is the first even term of the sequence.
		

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

Equals A079000 - 1.

Programs

Mathematica

a[0] = 0; a[n_] := With[{k = 2^Floor[Log[2, (n+4)/6]]}, (Abs[n - 9k + 4] - 3k + 3n + 6)/2 - 1];
Table[a[n], {n, 0, 70}] (* Jean-François Alcover, Aug 31 2018 *)

Formula

For a formula for a(n) see A079000.

a(a(n)) = 2n+4 for n >= 1.