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.

A097760 Index of zero values in A097759; also index of -1 values in A097563 and A097758.

Original entry on oeis.org

68, 81, 88, 95, 99, 104, 107, 115, 116, 118, 126, 134, 139, 149, 150, 152, 153, 157, 163, 164, 169, 177, 178, 180, 181, 184, 193, 197, 204, 207, 208, 209, 211, 212, 215, 217, 220, 225, 226, 227, 228, 229, 230, 231, 232, 236, 237, 238, 239, 244, 246, 247
Offset: 1

Views

Author

Ray Chandler, Sep 06 2004

Keywords

Comments

A097759(a(n))=0; A097758(a(n))=-1; A097563(a(n))=-1.

Crossrefs

Extensions

Offset changed to 1 by Jinyuan Wang, Aug 06 2021

A097757 Table read by rows where row n consists of integers that can be expressed as the sum of distinct squares in exactly n ways.

Original entry on oeis.org

2, 3, 6, 7, 8, 11, 12, 15, 18, 19, 22, 23, 24, 27, 28, 31, 32, 33, 43, 44, 47, 48, 60, 67, 72, 76, 92, 96, 108, 112, 128, 0, 1, 4, 5, 9, 10, 13, 14, 16, 17, 20, 21, 34, 35, 36, 37, 38, 39, 40, 42, 51, 52, 55, 56, 57, 58, 59, 63, 64, 68, 71, 73, 80, 83, 88, 97, 124, 132, 25, 26, 29
Offset: 0

Views

Author

Ray Chandler, Sep 06 2004

Keywords

Comments

Row 0 is A001422.
Only positive squares are allowed, not 0. The inclusion of 0 in row 1 is for the empty sum, not for a sum with a single 0. - Franklin T. Adams-Watters, Sep 20 2009

Examples

			Table begins:
Row 0: 2, 3, 6, 7, 8, 11, 12, 15, 18, 19, 22, 23, 24, 27, 28, 31, 32, 33, 43, 44, 47, 48, 60, 67, 72, 76, 92, 96, 108, 112, 128;
Row 1: 0, 1, 4, 5, 9, 10, 13, 14, 16, 17, 20, 21, 34, 35, 36, 37, 38, 39, 40, 42, 51, 52, 55, 56, 57, 58, 59, 63, 64, 68, 71, 73, 80, 83, 88, 97, 124, 132;
Row 2: 25, 26, 29, 30, 41, 45, 46, 49, 53, 54, 61, 69, 70, 77, 79, 82, 84, 87, 93, 103, 107, 133, 144, 148, 188;
Row 3: 50, 62, 66, 75, 81, 85, 86, 89, 91, 95, 98, 99, 100, 102, 104, 109, 113, 116, 118, 119, 123, 136, 137, 140, 152, 157, 172, 176, 177, 192;
Row 4: 65, 74, 78, 101, 105, 106, 111, 115, 117, 120, 121, 122, 127, 141, 153, 160, 164, 168, 193;
Row 5: 94, 125, 129, 131, 143, 145, 149, 156, 161, 163, 167, 173, 197, 213;
Row 6: 90, 114, 134, 135, 138, 139, 147, 180, 181, 208, 212, 217, 228;
Row 7: 110, 142, 151, 154, 158, 169, 184, 189, 204, 224;
Row 8: 155, 159, 162, 165, 166, 182, 187, 196, 201, 202, 203, 216, 229, 233, 240, 252, 253;
Row 9: 126, 130, 146, 150, 171, 178, 179, 183, 185, 200, 209, 236, 237, 241, 288;
Row 10: 191, 205, 218, 232, 249, 257;
Row 11: 170, 175, 198, 207, 220, 221, 227, 245, 272, 277, 293;
Row 12: 186, 214, 225, 244, 248, 268, 297;
Row 13: 174, 199, 223, 256, 265, 292;
Row 14: 190, 194, 206, 215, 261, 269, 273, 281, 313, 317;
Row 15: 211, 219, 242, 262, 301;
Row 16: 195, 222, 239, 243, 276, 278, 289, 333;
Row 17: 226, 230, 238, 264, 266, 284;
Row 18: 210, 258, 263, 267, 285, 304, 308, 337;
Row 19: 231, 246, 254, 260, 357;
Row 20: 234, 247, 251, 282, 305, 309, 353;
Row 21: 235, 250, 280, 298, 321, 329;
Row 22: 332.
Denoting r(n) the index of the row of the number n, among n = {350, ..., 1000} the only r-values below 28 are a(357) = 19, a(353) = 20, a(373) = 25, a(397) = 26, a(362) = 27, and all n >= 400 have r(n) > 30. So the above rows appear to be complete, and rows 23 & 24 would be empty, as would be rows 39 & 40 unless they have elements > 1000. - _M. F. Hasler_, May 26 2020
		

Crossrefs

Programs

  • PARI
    {r(n,m=n)=sum(x=1,min(sqrtint(n),m),r(n-x^2,x-1),!n)} \\ Gives index of the row in which number n is listed. - M. F. Hasler, May 26 2020

A097758 Greatest integer that can be written as a sum of distinct squares in exactly n ways, or -1 if no such number exists.

Original entry on oeis.org

128, 132, 188, 192, 193, 213, 228, 224, 253, 288, 257, 293, 297, 292, 317, 301, 333, 284, 337, 357, 353, 329, 332, 349, 336, 373, 397, 362, 393, 372, 377, 413, 368, 365, 388, 389, 417, 437, 433, 319, 343, 421, 405, 457, 453, 364, 408, 351, 432, 402, 473
Offset: 0

Views

Author

Ray Chandler, Sep 06 2004

Keywords

Comments

Trailing edge of table described in A097757; leading edge is A097563.

Crossrefs

Showing 1-3 of 3 results.