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

0,5

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.

Links

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

Formula

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

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

Example

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.

Prog

(Scheme, two alternative definitions)
(define (A244229 n) (- (A244224 n) 1))
(define (A244229 n) (- n (A244225 n)))

Crossrefs

One less than A244224 (partial sums of A244220).

Cf. A014418, A244220, A244222, A244225.

Sequence in context: A071823 A219642 A139338 * A317596 A057355 A171975

Adjacent sequences: A244226 A244227 A244228 * A244230 A244231 A244232

Keyword

nonn

Author

Antti Karttunen, Jun 25 2014

Status

approved