A381002 Gaston Tarry's 1905 trimagic square of order 128, read by rows.

16132, 130, 16381, 127, 16128, 382, 15873, 387, 13632, 2750, 13761, 2627, 13508, 2882, 13373, 3007, 8452, 7810, 8701, 7807, 8448, 8062, 8193, 8067, 11072, 5310, 11201, 5187, 10948, 5442, 10813, 5567, 10028, 6314, 10197, 6231, 9944, 6486, 9769, 6571, 13080, 3222, 13289

Offset

1,1

Comments

This is the first known trimagic square. It contains all numbers from 1 to 16384. The magic sum is 1048640; when each number is squared, the magic sum is 11454294720; and when each number is cubed, the magic sum is 140754668748800.

Terms are taken from Christian Boyer's Multimagie website (see links).

Links

Paolo Xausa, Table of n, a(n) for n = 1..16384

Christian Boyer, Trimagic square, 128th-order.

Brady Haran and Matt Parker, A Magic Square Breakthrough, YouTube Numberphile video, 2025.

Index entries for sequences related to magic squares

Example

The magic square is:
  [16132   130 16381   127 16128 ... 11854  4301 12111  4148 12210]
  [  128 16382   129 16131   388 ...  4402 12209  4147 12112  4302]
  [16002   260 15999   509 16254 ... 12240  4431 11981  4530 11828]
  [  510 16000   259 16001     2 ...  4276 11827  4529 11982  4432]
  [  257 16003   512 15998   253 ...  4175 11984  4430 11825  4531]
     ...   ...   ...   ...   ... ...   ...   ...   ...   ...   ...
  [ 4642 11684  4831 11613  5086 ...  7496  9159  7237  9018  7356]
  [ 4829 11615  4644 11682  4897 ...  7611  9020  7354  9157  7239]
  [11681  4643 11616  4830 11357 ...  8903  7240  9158  7353  9019]
  [ 4959 11485  5026 11300  4771 ...  7225  8890  7484  8775  7621]
  [11299  5025 11486  4960 11743 ...  9029  7622  8776  7483  8889]

Crossrefs

Cf. A052458, A380966, A381001.

Sequence in context: A335305 A267118 A145717 * A184405 A134120 A109566

Adjacent sequences: A380999 A381000 A381001 * A381003 A381004 A381005

Keyword

nonn,tabf,fini,full

Author

Paolo Xausa, Feb 13 2025

Status

approved