A244228 -id:A244228 - cp's OEIS frontend

A244223 Numbers k which have an odd representation in Greedy Catalan Base, i.e., where A014418(k) ends with digit one.

1, 3, 6, 8, 11, 13, 15, 17, 20, 22, 25, 27, 29, 31, 34, 36, 39, 41, 43, 45, 48, 50, 53, 55, 57, 59, 62, 64, 67, 69, 71, 73, 76, 78, 81, 83, 85, 87, 90, 92, 95, 97, 99, 101, 104, 106, 109, 111, 113, 115, 118, 120, 123, 125, 127, 129, 133, 135, 138, 140, 143, 145, 147, 149

Offset: 1

Antti Karttunen, Jun 23 2014

nonn

A244225 works as an inverse function for this injection. We have A244225(a(n)) = n for all n >= 1.

Antti Karttunen, Table of n, a(n) for n = 1..7118

Complement: A244222.
Characteristic function: A244221.
First differences: A244228.
Cf. A014418, A244161, A244225, A244227.

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

Antti Karttunen, Jun 23 2014

nonn

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.

			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.

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

Partial sums of A244221.

Cf. A014418, A244223, A244224, A244228, A244229.

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

Antti Karttunen, Jun 23 2014

nonn

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

Antti Karttunen, Table of n, a(n) for n = 0..7117

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.

Scheme
```
(define (A244227 n) (A244226 (+ n n)))
```

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

cp's OEIS Frontend

A244223 Numbers k which have an odd representation in Greedy Catalan Base, i.e., where A014418(k) ends with digit one.

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

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A244227 Even bisection of A244226.

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