A099627 -id:A099627 - cp's OEIS frontend

A167204 Triangle read by rows in which row n lists the first 2^(n-1) terms of A003602.

1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 3, 2, 4, 1, 1, 1, 2, 1, 3, 2, 4, 1, 5, 3, 6, 2, 7, 4, 8, 1, 1, 1, 2, 1, 3, 2, 4, 1, 5, 3, 6, 2, 7, 4, 8, 1, 9, 5, 10, 3, 11, 6, 12, 2, 13, 7, 14, 4, 15, 8, 16, 1, 1, 1, 2, 1, 3, 2, 4, 1, 5, 3, 6, 2, 7, 4, 8, 1, 9, 5, 10, 3, 11, 6, 12, 2, 13, 7, 14, 4, 15, 8, 16

Offset: 1

Alford Arnold, Nov 12 2009

The old definition (see history #7) was:

"Numbers such that n is contained in the array a(n) where array 1 is A099627, array 2 is A124922 etc. (Table A167979 illustrates the manner in which the array numbers are chosen - e.g. "12" is not in array 1 or 2 so it begins array 3. All of the arrays can be seen in A161924."

			From _Omar E. Pol_, Feb 21 2011: (Start)
If written as a triangle:
1,
1,1,
1,1,2,1,
1,1,2,1,3,2,4,1,
1,1,2,1,3,2,4,1,5,3,6,2,7,4,8,1,
1,1,2,1,3,2,4,1,5,3,6,2,7,4,8,1,9,5,10,3,11,6,12,2,13,7,14,4,15,8,16,1,
...
(End)
a(12)= 3 therefore, as expected, 12 is contained in array 3; a(14)= 4 so 14 is a member of array 4, etc.
A099627 (array 1) begins 1 2 3 4 5 7 8 9 11 15 ...
A124922 (array 2) begins 6 10 13 18 21 27 ... so a(n) begins 1 1 1 1 1 2 1 1 1 2 1 ...
The next two arrays begin 12 20 25 36 41 51 ... and 14 22 29 38 45 59 ...

Cf. A003602, A099627, A124922, A167201 (uses array 3), A167202 (uses array 4), A161924 (contains all of the arrays), A167979 (Linearizes and concatenates the arrays).

Definition corrected by Alford Arnold, Feb 05 2011
Better definition from Omar E. Pol, Feb 21 2011
Further edits from N. J. A. Sloane, Feb 21 2011
More terms a(64)-a(94) from Omar E. Pol, Feb 22 2011

A176577 Create a table by linearizing and concatenating arrays embedded in A114994 the terms of which map to numeric partitions.

Original entry on oeis.org

1, 2, 10, 3, 18, 36, 4, 21, 68, 42, 5, 34, 73, 74, 136, 7, 37, 132, 85, 264, 146, 8, 43, 137, 138, 273, 274, 170, 9, 66, 147, 149, 520, 293, 298, 292, 11, 69, 260, 171, 529, 530, 341, 548, 528, 15, 75, 265, 266, 547, 549, 554, 585, 1040, 546, 16, 87, 275, 277, 1032, 587

Offset: 1

Alford Arnold, Apr 20 2010

			The first embedded array is sequence A099629 = 1 2 3 4 5 7 8 9 11 15 ...
The second array begins 10 18 21 34 37 43 ...
and the table begins
1..10..36..42..136..146..170..292...
2..18..68..74..
3..21..73..85..
4..34..
5..37..
7..43..
The number 292 in binary is 100100100
which maps to partition 3+3+3.

Cf. A099627 A114994

A167979 (a similar array also mapped to numeric partitions) [From Alford Arnold, May 04 2010]

More terms from Alford Arnold, May 04 2010

A322795 Number of integers k, 0 <= k <= n, such that the Damerau-Levenshtein distance between the binary representations of n and k is strictly less than the Levenshtein distance.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 1, 2, 0, 0, 0, 1, 0, 2, 1, 3, 0, 4, 4, 4, 1, 4, 2, 4, 0, 0, 0, 1, 0, 2, 1, 3, 0, 4, 5, 5, 1, 5, 4, 7, 0, 8, 9, 9, 6, 8, 8, 8, 1, 8, 8, 8, 2, 8, 4, 8, 0, 0, 0, 1, 0, 2, 1, 4, 0, 4, 6, 6, 1, 5, 4, 9, 0, 8, 11, 11, 7, 10, 11, 11, 1, 10, 12, 13, 5, 13, 9, 14, 0, 16, 18, 17, 15, 16

Offset: 0

Pontus von Brömssen, Dec 26 2018

a(n) = 0 if and only if n appears in A099627 or n = 0.

a(n) = A079071(n) for n <= 21, but a(22) = 3 > 2 = A079071(22).

			For n = 6, the Damerau-Levenshtein distance and the Levenshtein distance between the binary representations of n and k are equal for all k <= n except k = 5. The Levenshtein distance between 101 and 110 (5 and 6 in binary) is 2, whereas the Damerau-Levenshtein distance is 1, so a(6) = 1.

Pontus von Brömssen, Table of n, a(n) for n = 0..1000
Wikipedia, Damerau-Levenshtein distance

Cf. A152487, A322285, A099627, A079071.

cp's OEIS Frontend

A167204 Triangle read by rows in which row n lists the first 2^(n-1) terms of A003602.

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A176577 Create a table by linearizing and concatenating arrays embedded in A114994 the terms of which map to numeric partitions.

Views

Author

Keywords

Examples

Crossrefs

Extensions

A322795 Number of integers k, 0 <= k <= n, such that the Damerau-Levenshtein distance between the binary representations of n and k is strictly less than the Levenshtein distance.

Views

Author

Keywords

Comments

Examples

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Crossrefs