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 1-4 of 4 results.

A256140 Square array read by antidiagonals upwards: T(n,k) = n^A000120(k), n>=0, k>=0.

Original entry on oeis.org

1, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 3, 2, 1, 0, 1, 4, 3, 4, 1, 0, 1, 5, 4, 9, 2, 1, 0, 1, 6, 5, 16, 3, 4, 1, 0, 1, 7, 6, 25, 4, 9, 4, 1, 0, 1, 8, 7, 36, 5, 16, 9, 8, 1, 0, 1, 9, 8, 49, 6, 25, 16, 27, 2, 1, 0, 1, 10, 9, 64, 7, 36, 25, 64, 3, 4, 1, 0, 1, 11, 10, 81, 8, 49, 36, 125, 4, 9, 4, 1, 0, 1, 12, 11, 100, 9, 64, 49, 216, 5, 16, 9, 8, 1, 0
Offset: 0

Views

Author

Omar E. Pol, Mar 16 2015

Keywords

Comments

The partial sums of row n give the n-th row of the square array A256141.
First differs from A244003 at a(25).

Examples

			The corner of the square array with the first 16 terms of the first 12 rows looks like this:
---------------------------------------------------------------------------
A000007: 1, 0, 0,  0,  0,  0,  0,   0,  0,  0,  0,   0,  0,   0,   0,    0
A000012: 1, 1, 1,  1,  1,  1,  1,   1,  1,  1,  1,   1,  1,   1,   1,    1
A001316: 1, 2, 2,  4,  2,  4,  4,   8,  2,  4,  4,   8,  4,   8,   8,   16
A048883: 1, 3, 3,  9,  3,  9,  9,  27,  3,  9,  9,  27,  9,  27,  27,   81
A102376: 1, 4, 4, 16,  4, 16, 16,  64,  4, 16, 16,  64, 16,  64,  64,  256
A256135: 1, 5, 5, 25,  5, 25, 25, 125,  5, 25, 25, 125, 25, 125, 125,  625
A256136: 1, 6, 6, 36,  6, 36, 36, 216,  6, 36, 36, 216, 36, 216, 216, 1296
.......: 1, 7, 7, 49,  7, 49, 49, 343,  7, 49, 49, 343, 49, 343, 343, 2401
.......: 1, 8, 8, 64,  8, 64, 64, 512,  8, 64, 64, 512, 64, 512, 512, 4096
.......: 1, 9, 9, 81,  9, 81, 81, 729,  9, 81, 81, 729, 81, 729, 729, 6561
.......: 1,10,10,100, 10,100,100,1000, 10,100,100,1000,100,1000,1000,10000
.......: 1,11,11,121, 11,121,121,1331, 11,121,121,1331,121,1331,1331,14641

Links

Crossrefs

Cf. A000120, A244003, A255740, A255741, A256141.
First seven rows are A000007, A000012, A001316, A048883, A102376, A256135, A256136.
First 16 columns are A000012, A001477, A001477, A000290, A001477, A000290, A000290, A000578, A001477, A000290, A000290, A000578, A000290, A000578, A000578, A000583.
Main diagonal gives A302451.

A256135 a(n) = 5^A000120(n).

Original entry on oeis.org

1, 5, 5, 25, 5, 25, 25, 125, 5, 25, 25, 125, 25, 125, 125, 625, 5, 25, 25, 125, 25, 125, 125, 625, 25, 125, 125, 625, 125, 625, 625, 3125, 5, 25, 25, 125, 25, 125, 125, 625, 25, 125, 125, 625, 125, 625, 625, 3125, 25, 125, 125, 625, 125, 625, 625, 3125, 125, 625, 625, 3125, 625, 3125, 3125, 15625
Offset: 0

Views

Author

Omar E. Pol, Mar 19 2015

Keywords

Comments

Also, a row of the square array A256140.
It appears that when A151780 is regarded as a triangle in which the row lengths are the powers of 2, this is what the rows converge to.

Examples

			Also, written as an irregular triangle in which the row lengths are the terms of A011782, the sequence begins:
1;
5;
5, 25;
5, 25, 25, 125;
5, 25, 25, 125, 25, 125, 125, 625;
...

Crossrefs

Cf. A000120, A001316, A048883, A102376, A130667, A151780, A256140, A256141.

Programs

Formula

a(n) = A000351(A000120(n)). - Michel Marcus, Mar 21 2015
G.f.: Product_{k>=0} (1 + 5*x^(2^k)). - Ilya Gutkovskiy, Feb 28 2017

Extensions

More terms from Michael De Vlieger, Mar 20 2015

A161343 a(n) = 7^A000120(n).

Original entry on oeis.org

1, 7, 7, 49, 7, 49, 49, 343, 7, 49, 49, 343, 49, 343, 343, 2401, 7, 49, 49, 343, 49, 343, 343, 2401, 49, 343, 343, 2401, 343, 2401, 2401, 16807, 7, 49, 49, 343, 49, 343, 343, 2401, 49, 343, 343, 2401, 343, 2401, 2401, 16807, 49, 343, 343, 2401, 343, 2401, 2401, 16807, 343, 2401, 2401, 16807, 2401, 16807, 16807, 117649
Offset: 0

Views

Author

Omar E. Pol, Jun 14 2009

Keywords

Comments

Also first differences of A161342.
From Omar E. Pol, May 03 2015: (Start)
It appears that when A151785 is regarded as a triangle in which the row lengths are the powers of 2, this is what the rows converge to.
Also this is also a row of the square array A256140.
(End)

Examples

			From _Omar E. Pol_, May 03 2015: (Start)
Also, written as an irregular triangle in which the row lengths are the terms of A011782, the sequence begins:
1;
7;
7, 49;
7, 49, 49, 343;
7, 49, 49, 343, 49, 343, 343, 2401;
7, 49, 49, 343, 49, 343, 343, 2401, 49, 343, 343, 2401, 343, 2401, 2401, 16807;
...
Row sums give A055274.
Right border gives A000420.
(End)

Links

Crossrefs

Cf. A000420, A011782, A055274, A160410, A151785, A161411, A160428, A160429, A161342, A256140, A256141.
Rows of the array A256140 are: A000007, A000012, A001316, A048883, A102376, A256135, A256136, this sequence.

Programs

  • PARI
    a(n) = 7^hammingweight(n); \\ Omar E. Pol, May 03 2015

Formula

a(n) = A000420(A000120(n)). - Omar E. Pol, May 03 2015
G.f.: Product_{k>=0} (1 + 7*x^(2^k)). - Ilya Gutkovskiy, Mar 02 2017

Extensions

More terms from Sean A. Irvine, Mar 08 2011
New name from Omar E. Pol, May 03 2015
a(52)-a(63) from Omar E. Pol, May 16 2015

A256136 a(n) = 6^A000120(n).

Original entry on oeis.org

1, 6, 6, 36, 6, 36, 36, 216, 6, 36, 36, 216, 36, 216, 216, 1296, 6, 36, 36, 216, 36, 216, 216, 1296, 36, 216, 216, 1296, 216, 1296, 1296, 7776, 6, 36, 36, 216, 36, 216, 216, 1296, 36, 216, 216, 1296, 216, 1296, 1296, 7776, 36, 216, 216, 1296, 216, 1296, 1296, 7776, 216, 1296, 1296, 7776, 1296, 7776
Offset: 0

Views

Author

Omar E. Pol, Mar 19 2015

Keywords

Comments

Also, a row of the square array A256140.
It appears that when A151784 is regarded as a triangle in which the row lengths are the powers of 2, this is what the rows converge to.

Examples

			Also, written as an irregular triangle in which the row lengths are the terms of A011782, the sequence begins:
1;
6;
6, 36;
6, 36, 36, 216;
6, 36, 36, 216, 36, 216, 216, 1296;
...

Crossrefs

Cf. A000120, A001316, A048883, A102376, A116522, A151784, A256135, A256140, A256141.

Programs

Formula

a(n) = A000400(A000120(n)). - Michel Marcus, Mar 21 2015
G.f.: Product_{k>=0} (1 + 6*x^(2^k)). - Ilya Gutkovskiy, Feb 28 2017

Extensions

More terms from Michael De Vlieger, Mar 20 2015
Showing 1-4 of 4 results.

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