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.

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A152089 Numbers k such that k! is not the sum of two nonnegative triangular numbers.

Original entry on oeis.org

6, 11, 12, 14, 18, 19, 20, 22, 23, 25, 26, 30, 31, 35, 36, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 55, 56, 57, 58, 60, 61, 62, 63, 64, 65, 67, 69, 70, 71, 73, 74, 75, 76, 77, 78, 82, 83, 84, 87, 88, 89, 90, 91, 92, 93, 94, 97, 98, 100, 101, 103, 104, 105, 106, 107, 108
Offset: 1

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Author

N. J. A. Sloane, Sep 24 2010

Keywords

Comments

Up to 300 these are also terms: 110, 111, 112, 113, 115, 116, 117, 119, 120, 121, 122, 123, 124, 127, 128, 130, 132, 136, 137, 138, 142, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 163, 166, 167, 168, 169, 170, 172, 174, 175, 176, 177, 179, 180, 181, 182, 183, 185, 186, 187, 188, 191, 193, 194, 195, 196, 197, 198, 200, 201, 202, 203, 204, 205, 206, 207, 210, 211, 213, 214, 215, 216, 218, 223, 225, 226, 227, 228, 229, 230, 231, 232, 236, 237, 238, 239, 240, 241, 243, 245, 246, 247, 249, 250, 251, 253, 255, 256, 257, 258, 260, 261, 262, 263, 265, 266, 267, 269, 270, 271, 272, 273, 274, 276, 278, 279, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 292, 293, 294, 295, 297, 298. - G. Guninski, Oct 12 2010

Links

Crossrefs

Complement of A180590.
Cf. A051611.

Extensions

69 added by N. J. A. Sloane, Sep 24 2010 using the data from the Factor Database web site.
Further terms from G. Guninski and D. S. McNeil, Sep 24 2010
Terms from 93 on from G. Guninski, Oct 12 2010

A171099 a(n) = number of solutions (x,y) (with 0 <= x <= y) to x*(x+1)/2 + y*(y+1)/2 = n!.

Original entry on oeis.org

1, 1, 1, 2, 1, 2, 0, 1, 1, 1, 2, 0, 0, 1, 0, 2, 1, 2, 0, 0, 0, 2, 0, 0, 2, 0, 0, 8, 1, 2, 0, 0, 4, 4, 16, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 1, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 2, 0, 16, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 16, 2, 4, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0
Offset: 0

Views

Author

N. J. A. Sloane, Sep 24 2010, based on a posting by R. K. Guy to the Sequence Fans Mailing List, Sep 10 2010

Keywords

Examples

			Initial solutions: (x,y,n) = (0,1,0), (0,1,1), (1,1,2), (0,3,3), (2,2,3), (2,6,4), (0,15,5), (5,14,5), (45,89,7), (89,269,8), (210,825,9), (760,2610,10), (1770,2030,10), none for n = 11 or 12, one for n = 13 (71504,85680,13) (found by _Ed Pegg Jr_), etc.

Crossrefs

Cf. A000161, A152089 (n for which no solutions exist), A180590 (n for which solutions exist).

Formula

a(n) = A000161(8*n! + 2). - Max Alekseyev, Dec 12 2011

Extensions

Corrected and extended (with data from Georgi Guninski, at the suggestion of N. J. A. Sloane) by D. S. McNeil, Sep 26 2010
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Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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