A244225 a(n) = Number of nonnegative integers 0 <= k <= n, which have an odd representation in Greedy Catalan Base (A014418).

0, 1, 1, 2, 2, 2, 3, 3, 4, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 10, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 14, 15, 15, 16, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20, 20, 21, 21, 22, 22, 22, 23, 23, 24, 24, 25, 25, 26, 26, 26, 27, 27, 28, 28, 28, 29, 29, 30, 30, 31, 31, 32, 32, 32

Offset: 0

Author

Antti Karttunen, Jun 23 2014

Keywords

• nonn

Comments

This works also as an inverse function for injection A244223: we have a(A244223(n)) = n for all n >= 1.

Equally, for n >= 1, a(n) = the largest k such that A244223(k) <= n.

After 0, each n occurs A244228(n) times.

Examples

			The first nonnegative integers represented in Greedy Catalan Base look like:
A014418(0) = 0
A014418(1) = 1
A014418(2) = 10
A014418(3) = 11
A014418(4) = 20
A014418(5) = 100
A014418(6) = 101
Of these, the first "odd" representation (ending with one) occurs at n=1, thus a(0) = 0, but a(1) = 1. As the next odd occurs at n=3, also a(2) = 1, but a(3) = 1+1 = 2. The next odd representation does not occur until at n=6, thus a(4) = a(5) = 2 and a(6) = 3.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 0..4862

Crossrefs

Partial sums of A244221.

Cf. A014418, A244223, A244224, A244228, A244229.

Formula

a(n) = n - A244229(n).