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.

A280288 Numbers n such that number of partitions of n is even and number of partitions of n into distinct parts is odd.

Original entry on oeis.org

2, 15, 22, 26, 40, 57, 70, 100, 117, 126, 176, 187, 247, 260, 532, 551, 590, 651, 715, 782, 925, 950, 1001, 1027, 1080, 1107, 1162, 1276, 1365, 1457, 1520, 1552, 1650, 1751, 1820, 1926, 2072, 2185, 2262, 2301, 2380, 2420, 2501, 2667, 2752, 2926, 3015, 3060, 3151, 3290, 3432, 3577, 3725, 3927, 4082, 4187, 4240, 4401
Offset: 1

Views

Author

Ilya Gutkovskiy, Dec 31 2016

Keywords

Comments

Intersection of A001318 and A001560.
Numbers n such that A000035(A000041(n)) = 0 and A000035(A000009(n)) = 1.

Examples

			15 is in the sequence because we have:
------------------------------------
number of partitions = 176 (is even)
------------------------------------
15 = 15
14 + 1 = 15
13 + 2 = 15
13 + 1 + 1 = 15
12 + 3 = 15
12 + 2 + 1 = 15
12 + 1 + 1 + 1 = 15
11 + 4 = 15
11 + 3 + 1 = 15
11 + 2 + 2 = 15
11 + 2 + 1 + 1 = 15
11 + 1 + 1 + 1 + 1 = 15
...
------------------------------------------------------
number of partitions into distinct parts = 27 (is odd)
------------------------------------------------------
15 = 15
14 + 1 = 15
13 + 2 = 15
12 + 3 = 15
12 + 2 + 1 = 15
11 + 4 = 15
11 + 3 + 1 = 15
10 + 5 = 15
10 + 4 + 1 = 15
10 + 3 + 2 = 15
...

Links

Crossrefs

Cf. A000009, A000035, A000041, A001318, A001560, A280289, A280290, A280291.

Programs

  • Mathematica
    Select[Range[4500], Mod[PartitionsP[#1], 2] == 0 && Mod[PartitionsQ[#1], 2] == 1 & ]

A280290 Numbers n such that number of partitions of n is even and number of partitions of n into distinct parts is even.

Original entry on oeis.org

8, 9, 10, 11, 19, 21, 25, 27, 28, 30, 31, 34, 42, 45, 46, 47, 50, 55, 58, 59, 62, 64, 65, 66, 74, 75, 78, 79, 80, 84, 86, 94, 96, 97, 98, 101, 103, 106, 108, 109, 110, 112, 113, 116, 120, 122, 124, 125, 128, 129, 130, 131, 133, 135, 136, 137, 141, 142, 147, 149, 151, 153, 154, 158, 160, 163, 167, 170, 171, 174, 175, 179, 180
Offset: 1

Views

Author

Ilya Gutkovskiy, Dec 31 2016

Keywords

Comments

Intersection of A001560 and A090864.
Numbers n such that A000035(A000041(n)) = 0 and A000035(A000009(n)) = 0.

Examples

			8 is in the sequence because we have:
-----------------------------------
number of partitions = 22 (is even)
-----------------------------------
8 = 8
7 + 1 = 8
6 + 2 = 8
6 + 1 + 1 = 8
5 + 3 = 8
5 + 2 + 1 = 8
5 + 1 + 1 + 1 = 8
4 + 4 = 8
4 + 3 + 1 = 8
4 + 2 + 2 = 8
4 + 2 + 1 + 1 = 8
4 + 1 + 1 + 1 + 1 = 8
3 + 3 + 2 = 8
3 + 3 + 1 + 1 = 8
3 + 2 + 2 + 1 = 8
3 + 2 + 1 + 1 + 1 = 8
3 + 1 + 1 + 1 + 1 + 1 = 8
2 + 2 + 2 + 2 = 8
2 + 2 + 2 + 1 + 1 = 8
2 + 2 + 1 + 1 + 1 + 1 = 8
2 + 1 + 1 + 1 + 1 + 1 + 1 = 8
1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 8
-------------------------------------------------------
number of partitions into distinct parts = 6 (is even)
-------------------------------------------------------
8 = 8
7 + 1 = 8
6 + 2 = 8
5 + 3 = 8
5 + 2 + 1 = 8
4 + 3 + 1 = 8

Links

Crossrefs

Cf. A000009, A000035, A000041, A001560, A090864, A280288, A280289, A280291.

Programs

  • Mathematica
    Select[Range[180], Mod[PartitionsP[#1], 2] == Mod[PartitionsQ[#1], 2] == 0 & ]

A280291 Numbers n such that number of partitions of n is odd and number of partitions of n into distinct parts is odd.

Original entry on oeis.org

0, 1, 5, 7, 12, 35, 51, 77, 92, 145, 155, 210, 222, 287, 301, 330, 345, 376, 392, 425, 442, 477, 495, 610, 672, 737, 805, 852, 876, 1190, 1247, 1335, 1426, 1617, 1717, 1855, 1962, 2035, 2147, 2542, 2625, 2795, 2882, 3197, 3337, 3480, 3626, 3775, 3876, 4030, 4347, 4510, 4565, 4845, 4902
Offset: 1

Views

Author

Ilya Gutkovskiy, Dec 31 2016

Keywords

Comments

Intersection of A001318 and A052002.
Numbers n such that A000035(A000041(n)) = 1 and A000035(A000009(n)) = 1.

Examples

			7 is in the sequence because we have:
----------------------------------
number of partitions = 15 (is odd)
----------------------------------
7 = 7
6 + 1 = 7
5 + 2 = 7
5 + 1 + 1 = 7
4 + 3 = 7
4 + 2 + 1 = 7
4 + 1 + 1 + 1 = 7
3 + 3 + 1 = 7
3 + 2 + 2 = 7
3 + 2 + 1 + 1 = 7
3 + 1 + 1 + 1 + 1 = 7
2 + 2 + 2 + 1 = 7
2 + 2 + 1 + 1 + 1 = 7
2 + 1 + 1 + 1 + 1 + 1 = 7
1 + 1 + 1 + 1 + 1 + 1 + 1 = 7
-----------------------------------------------------
number of partitions into distinct parts = 5 (is odd)
-----------------------------------------------------
7 = 7
6 + 1 = 7
5 + 2 = 7
4 + 3 = 7
4 + 2 + 1 = 7

Links

Crossrefs

Cf. A000009, A000035, A000041, A001318, A052002, A280288, A280289, A280290.

Programs

  • Mathematica
    Join[{0}, Select[Range[5000], Mod[PartitionsP[#1], 2] == Mod[PartitionsQ[#1], 2] == 1 & ]]

Extensions

a(1)=0 inserted by Alois P. Heinz, Dec 31 2016
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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