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 1-8 of 8 results.

A265141 Irregular table read by rows: n-th row lists the 9 n-gonal numbers of a 3 X 3 semimagic square with the smallest magic sum. The terms of each row are arranged in the manner shown in A261816.

Original entry on oeis.org

15, 66, 630, 231, 435, 45, 465, 210, 36, 16, 529, 2704, 1024, 1936, 289, 2209, 784, 256, 651, 54626, 356972, 135751, 241001, 35497, 275847, 116622, 19780, 6, 39621, 481671, 158766, 345696, 16836, 362526, 135981, 22791, 697, 93799, 662290, 298771, 448804, 9211, 457318, 214183, 85285
Offset: 3

Views

Author

Arkadiusz Wesolowski, Dec 02 2015

Keywords

Comments

The squares presented in this sequence are basic semimagic. For a definition of basic semimagic squares, see A261816.
The magic constants are, respectively: 711 = A269060(1), 3249 = 57^2 = A269061(1), and 412249.

Examples

			The semimagic squares are:
triangular numbers
|---|---|---|
| 15| 66|630|
|---|---|---|
|231|435| 45|
|---|---|---|
|465|210| 36|
|---|---|---|
.
square numbers
|----|----|----|
| 16 | 529|2704|
|----|----|----|
|1024|1936| 289|
|----|----|----|
|2209| 784| 256|
|----|----|----|
.
pentagonal numbers
|------|------|------|
|  651 | 54626|356972|
|------|------|------|
|135751|241001| 35497|
|------|------|------|
|275847|116622| 19780|
|------|------|------|

Links

Crossrefs

Cf. A269060, A269061, A265142.

Extensions

More terms from Arkadiusz Wesolowski, Apr 03 2016

A269060 Magic sums of 3 X 3 semimagic squares composed of positive triangular numbers.

Original entry on oeis.org

711, 1251, 1712, 2132, 2616, 2812, 2934, 3357, 3441, 3781, 3812, 4156, 4288, 4842, 4971, 4972, 5346, 5382, 5659, 5842, 5886, 6147, 6159, 6402, 6734, 7062, 7312, 7403, 7592, 7722, 8034, 8342, 8831, 8862, 8961, 9092, 9117, 9496, 9987, 10066, 10261, 10341
Offset: 1

Views

Author

Arkadiusz Wesolowski, Feb 18 2016

Keywords

Examples

			A semimagic square with sum 711:
  |----|----|----|
  | 15 | 66 |630 |
  |----|----|----|
  |231 |435 | 45 |
  |----|----|----|
  |465 |210 | 36 |
  |----|----|----|

Links

Crossrefs

Subsequence of A265197 and A269062.
Cf. A000217, A265141, A269061.

A269062 Magic sums of 3 X 3 semimagic squares composed of positive triangular numbers and squares.

Original entry on oeis.org

136, 146, 161, 175, 200, 230, 236, 250, 263, 277, 280, 290, 301, 316, 317, 326, 340, 346, 355, 370, 382, 394, 395, 398, 406, 410, 416, 421, 425, 431, 434, 436, 445, 446, 450, 461, 470, 472, 481, 484, 487, 494, 497, 499, 502, 511, 515, 518, 520, 527, 530
Offset: 1

Views

Author

Arkadiusz Wesolowski, Feb 18 2016

Keywords

Examples

			A semimagic square with sum 136:
  |----|----|----|
  |  6 | 25 |105 |
  |----|----|----|
  | 49 | 66 | 21 |
  |----|----|----|
  | 81 | 45 | 10 |
  |----|----|----|

Links

Crossrefs

Cf. A269060, A269061.

A265198 Magic sums of 3 X 3 semimagic squares composed of squares.

Original entry on oeis.org

3249, 3969, 4225, 5041, 5691, 6241, 6561, 7225, 7329, 8281, 8649, 8841, 9025, 9801, 10011, 10794, 11025, 11306, 11449, 11881, 12219, 12321, 12769, 12996, 13689, 13699, 13701, 14114, 14161, 14641, 15129, 15625, 15876, 16129, 16186, 16625, 16641, 16900
Offset: 1

Views

Author

Arkadiusz Wesolowski, Dec 04 2015

Keywords

Comments

These semimagic squares are composed of 9 distinct square numbers >= 0.

Examples

			A semimagic square with sum 4225:
  |----|----|----|
  |  0 | 625|3600|
  |----|----|----|
  |1521|2304| 400|
  |----|----|----|
  |2704|1296| 225|
  |----|----|----|

Links

Crossrefs

Cf. A000290, A265141, A265197, A269061 (for positive squares).

A269297 Magic sums of 3 X 3 semimagic squares composed of odd squares.

Original entry on oeis.org

5691, 10011, 12219, 13699, 17059, 19891, 20931, 22499, 23475, 26859, 27531, 30251, 30499, 33251, 34307, 38739, 39771, 39779, 40275, 42771, 43059, 45275, 46739, 47091, 49179, 49275, 51219, 53875, 53979, 56499, 58499, 59227, 60739, 61779, 64275, 64819
Offset: 1

Views

Author

Arkadiusz Wesolowski, Feb 21 2016

Keywords

Links

Crossrefs

Cf. A016754, A265197. Subsequence of A269061.

Formula

a(n) = 8*A265197(n) + 3.

A271021 Magic sums of 3 X 3 semimagic squares of squares whose rows, columns, and at least one of the two main diagonals sum to the same number.

Original entry on oeis.org

21609, 86436, 194481, 257049, 345744, 540225, 777924, 1028196, 1058841, 1172889, 1382976, 1750329, 2160900, 2313441, 2614689, 3111696, 3651921, 4112784, 4235364, 4691556, 4862025, 5531904, 6245001, 6426225, 7001316, 7800849, 8311689, 8643600, 9253764, 9529569
Offset: 1

Views

Author

Arkadiusz Wesolowski, Mar 28 2016

Keywords

Links

Crossrefs

Cf. A267118, A271020, A271022. Subsequence of A269061. Supersequence of A271022.

A265142 a(n) = smallest magic sum of any 3 X 3 semimagic square composed of n-gonal numbers.

Original entry on oeis.org

711, 3249, 412249, 521298, 756786, 1076461
Offset: 3

Views

Author

Arkadiusz Wesolowski, Dec 02 2015

Keywords

Links

Crossrefs

Cf. A269060, A269061, A265141.

Formula

a(n) = Sum_{k=1..3} A265141(n,k).

Extensions

a(6)-a(8) from Arkadiusz Wesolowski, Apr 03 2016

A269344 Magic sums of 3 X 3 semimagic squares composed of squares of primes.

Original entry on oeis.org

5691, 26859, 27531, 85659, 93219, 111699, 113331, 155739, 179091, 203571, 228459, 239379, 277419, 281499, 344931, 376971, 469011, 487491, 490299, 520491, 583779, 631491, 679539, 806547, 851211, 896091, 922659, 1004379, 1067619, 1099539, 1119459, 1134771
Offset: 1

Views

Author

Arkadiusz Wesolowski, Apr 16 2016

Keywords

Examples

			Examples of 3 X 3 semimagic squares composed of squares of primes.
.
|-----|-----|-----|
| 11^2| 23^2| 71^2|
|-----|-----|-----|
| 43^2| 59^2| 19^2|
|-----|-----|-----|
| 61^2| 41^2| 17^2|
|-----|-----|-----|
The magic constant is 5691 = a(1).
.
|-----|-----|-----|
| 13^2| 67^2|149^2|
|-----|-----|-----|
| 89^2|127^2| 53^2|
|-----|-----|-----|
|137^2| 79^2| 43^2|
|-----|-----|-----|
The magic constant is 26859 = a(2).

Links

Crossrefs

Cf. A269061. Subsequence of A269297.
Showing 1-8 of 8 results.

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