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.

A271581 Magic sums of 4 X 4 magic squares composed of triangular numbers and squares.

Original entry on oeis.org

251, 305, 317, 341, 362, 366, 371, 377, 387, 389, 410, 421, 427, 431, 434, 435, 440, 446, 455, 458, 470, 482, 483, 484, 490, 494, 497, 500, 506, 512, 515, 519, 521, 523, 525, 536, 546, 547, 548, 550, 551, 553, 563, 566, 572, 575, 578, 580, 584, 586, 590, 591
Offset: 1

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Author

Arkadiusz Wesolowski, Apr 10 2016

Keywords

Examples

			Examples of 4 X 4 magic squares composed of triangular numbers and squares.
.
|---|---|---|---|
| 6 | 10|210| 25|
|---|---|---|---|
| 81|121| 21| 28|
|---|---|---|---|
| 64|105| 4 | 78|
|---|---|---|---|
|100| 15| 16|120|
|---|---|---|---|
The magic constant is 251 = a(1).
.
|---|---|---|---|
| 4 | 10| 81|210|
|---|---|---|---|
|105|144| 55| 1 |
|---|---|---|---|
|171| 15| 91| 28|
|---|---|---|---|
| 25|136| 78| 66|
|---|---|---|---|
The magic constant is 305 = a(2).

Links

Crossrefs

Cf. A271578, A271579.

A272303 Magic sums of 4 X 4 semimagic squares composed of primes.

Original entry on oeis.org

114, 120, 124, 126, 130, 132, 136, 138, 140, 142, 144, 146, 148, 150, 152, 154, 156, 158, 160, 162, 164, 166, 168, 170, 172, 174, 176, 178, 180, 182, 184, 186, 188, 190, 192, 194, 196, 198, 200, 202, 204, 206, 208, 210, 212, 214, 216, 218, 220, 222, 224, 226
Offset: 1

Views

Author

Arkadiusz Wesolowski, Apr 25 2016

Keywords

Comments

In other words, numbers n such that there is a 4 X 4 semimagic square of primes with magic sum n.
Conjecture: every even number greater than 134 belongs to this sequence.

Examples

			Examples of 4 X 4 semimagic squares composed of primes.
.
|---|---|---|---|
| 3 | 11| 47| 53|
|---|---|---|---|
| 23| 37| 41| 13|
|---|---|---|---|
| 29| 61| 7 | 17|
|---|---|---|---|
| 59| 5 | 19| 31|
|---|---|---|---|
The magic constant is 114 = a(1).
.
|---|---|---|---|
| 3 | 5 | 23| 89|
|---|---|---|---|
| 17| 53| 37| 13|
|---|---|---|---|
| 41| 43| 29| 7 |
|---|---|---|---|
| 59| 19| 31| 11|
|---|---|---|---|
The magic constant is 120 = a(2).

Links

Crossrefs

Cf. A270864. Supersequence of A271578.

Formula

If conjecture is true, a(n) = A005843(n+61) for n >= 7.

A368676 Number of 4 X 4 prime magic squares with magic sum 2n.

Original entry on oeis.org

128, 0, 0, 160, 0, 0, 224, 0, 64, 384, 64, 192, 2112, 96, 224, 4768, 0, 480, 5472, 160, 1088, 6688, 160, 1632, 13600, 416, 1728, 24640, 544, 3008, 40736, 512, 6720, 45504, 672, 11776, 41984, 2752, 17888, 65760, 4416, 18688, 128544, 4544, 21888, 162240, 3712
Offset: 60

Views

Author

Zhao Hui Du, Jan 02 2024

Keywords

Examples

			[17, 11, 31, 61]
[43, 67,  3,  7]
[41, 37, 13, 29]
[19,  5, 73, 23]
 is a 4 X 4 prime magic square in which the elements in each row and column and both diagonals sum to 120 and all elements are prime numbers. There are a total of 128 such prime magic squares so a(60)=128.

Links

Crossrefs

Cf. A006052, A073520, A073521, A271578.
Showing 1-3 of 3 results.

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

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