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 A244229 a(n) = Number of integers 0 < k <= n, which have an even representation in Greedy Catalan Base (A014418). 4
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified June 9 19:10 EDT 2023. Contains 363183 sequences. (Running on oeis4.)