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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

Original entry on oeis.org

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

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Author

Antti Karttunen, Jun 23 2014

Keywords

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

Crossrefs

Partial sums of A244221.
Cf. A014418, A244223, A244224, A244228, A244229.

Formula

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

A244222 Numbers k which have even representation in Greedy Catalan Base, i.e., where A014418(k) ends with zero.

Original entry on oeis.org

0, 2, 4, 5, 7, 9, 10, 12, 14, 16, 18, 19, 21, 23, 24, 26, 28, 30, 32, 33, 35, 37, 38, 40, 42, 44, 46, 47, 49, 51, 52, 54, 56, 58, 60, 61, 63, 65, 66, 68, 70, 72, 74, 75, 77, 79, 80, 82, 84, 86, 88, 89, 91, 93, 94, 96, 98, 100, 102, 103, 105, 107, 108, 110, 112, 114, 116, 117, 119, 121, 122, 124, 126, 128, 130, 131, 132
Offset: 0

Views

Author

Antti Karttunen, Jun 23 2014

Keywords

Comments

A244229 works as an inverse function for this injection. We have A244229(a(n)) = n for all n.

Links

Crossrefs

Complement: A244223.
Characteristic function: A244220.
Cf. A244221, A244229, A014418, A244161.

A244224 a(n) = Number of nonnegative integers 0 <= k <= n, which have an even representation in Greedy Catalan Base (A014418).

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Jun 23 2014

Keywords

Comments

The terms a(0) .. a(23) are equal to A076905(1) .. A076905(24).

Examples

			The first nonnegative integers represented in Greedy Catalan Base look like this:
A014418(0) = 0
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=0, thus a(0) = 1, and as 1 is odd, also a(1) = 1. The next even occurs at n=2, so a(2) = 2. The next even representations after that occur at n=4, 5 and 7, thus a(3) = 2, a(4) = 3, a(5) = 4, a(6) = 4 and a(7) = 5.

Links

Crossrefs

Partial sums of A244220.
One more than A244229.
Cf. A244225, A076905.
Showing 1-3 of 3 results.

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