cp's OEIS Frontend

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.

A167979 Linearize the arrays A099627 A124922 ... defined in A167204 and based on A161924 then concatenate to form a new table.

Original entry on oeis.org

1, 2, 6, 3, 10, 12, 4, 13, 20, 14, 5, 18, 25, 22, 24, 7, 21, 36, 29, 40, 26, 8, 27, 41, 38, 49, 42, 28, 9, 34, 51, 45, 72, 53, 44, 30, 11, 37, 68, 59, 81, 74, 57, 46, 48, 15, 43, 73, 70, 99, 85, 76, 61, 80, 50, 16, 55, 83, 77, 136, 107, 89, 78, 97, 82, 52
Offset: 1

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Author

Alford Arnold, Nov 15 2009

Keywords

Comments

Contribution from Alford Arnold, Nov 29 2009: (Start)
Note that the values within A167977 identify the number partitioned described in A125106 and A161924.
(End)

Examples

			The resulting table begins:
..1..2..3..4..5..7..8
..6.10.13.18.21.27
.12.20.25.36.41
.14.22.29.38
etc.
Contribution from _Alford Arnold_, Nov 29 2009: 4 equals 2+2 which maps to the natural number 6 (binary 110) and 6 appears in the second array (A124922).

Crossrefs

Cf. A099627 A124922 A167204 A161924
Contribution from Alford Arnold, Nov 29 2009: (Start)
A125106(Describes the mapping to partitions). A167977 is A161511(A167979).
(End)

Extensions

Corrected By Alford Arnold, Nov 29 2009

A167202 Fourth in a series of triangular subarrays of A117506. Previous arrays are Tables A007318, A059797 and A167201.

Original entry on oeis.org

5, 21, 14, 56, 70, 28, 120, 216, 162, 48
Offset: 1

Views

Author

Alford Arnold, Nov 04 2009

Keywords

Comments

This subarray is generated from values related to the source partition
2+2+2. (cf A161924). Note that A117506(25) maps to Partition 2+2+2
which corresponds to the 14th natural number appearing in A161924.
Note also that Table A167201 is the transpose of Table a(n) and that
partition 3+3 is the conjugate of partition 2+2+2.

Examples

			The A161924 domain values begin:
14
22..29
38..45..59
70..77..91..119
so based on function A117506, a(n) begins:
5
21..14
56..70..28
70..77..91..119

Crossrefs

A099627 A007318 A124922 A059797 A161924 A167201 A117506

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

Original entry on oeis.org

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

Views

Author

Alford Arnold, Nov 12 2009

Keywords

Comments

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."

Examples

			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 ...

Crossrefs

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

Extensions

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
Showing 1-3 of 3 results.

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