A244229 a(n) = Number of integers 0 < k <= n, which have an even representation in Greedy Catalan Base (A014418).

0, 0, 1, 1, 2, 3, 3, 4, 4, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 11, 11, 12, 12, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 19, 19, 20, 20, 21, 22, 22, 23, 23, 24, 24, 25, 25, 26, 27, 27, 28, 28, 29, 30, 30, 31, 31, 32, 32, 33, 33, 34, 35, 35, 36, 36, 37, 38, 38, 39, 39, 40, 40, 41, 41, 42

Offset: 0

Author

Antti Karttunen, Jun 25 2014

Keywords

• nonn

Comments

This works as an inverse function for the injection A244222. We have a(A244222(n)) = n for all n.

Equally, for n >= 0, a(n) = the largest k such that A244222(k) <= n.

Examples

			The first positive numbers in Greedy Catalan Base representation are:
A014418(1) = 1
A014418(2) = 10
A014418(3) = 11
A014418(4) = 20
A014418(5) = 100
A014418(6) = 101
A014418(7) = 110
Of these, the first "even" representation (ending with zero) occurs at n=2, thus a(0) = a(1) = 0, and a(2) = 1. The next even representations occur at n=4, 5 and 7, thus a(3) = 1, a(4) = 2, a(5) = 3, a(6) = 3 and a(7) = 4.
		

Links

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

Crossrefs

One less than A244224 (partial sums of A244220).

Cf. A014418, A244220, A244222, A244225.

Formula

a(n) = A244224(n)-1.

a(n) = n - A244225(n).