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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.

Showing 1-3 of 3 results.

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).

A244227 Even bisection of A244226.

Original entry on oeis.org

1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 3, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 3, 1, 2, 1, 2, 1, 1, 1, 2
Offset: 0

Views

Author

Antti Karttunen, Jun 23 2014

Keywords

Comments

Number of integers in the n-th run of successive integers having an "even" representation in the Greedy Catalan Base: A244222.

Links

Crossrefs

One less than A244228.
Cf. A244222, A244224, A244226.
Differs from A131718 for the first time at n=56, as here a(56) = 3 while A131718(56) = 2.

Programs

Formula

a(n) = A244226(2*n).

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

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Jun 25 2014

Keywords

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

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).
Showing 1-3 of 3 results.

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