A137317 Array T(n,m) = 1 + (n+m-2) mod 26, 1 <= n,m <= 26, read by rows or columns.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22

Offset

1,2

Comments

The pattern arises if one assigns numbers A=1 up to Z=26 to the letters in the 26 X 26 Vigenere square, which contains A to Z in the first row and circular shifts in the follow-up rows (that is, B..Z,A in the 2nd, C...Z,A,B in the 3rd etc.).

References

Blaise de Vigenere, Traicte des chiffres ou secretes manieres d'ecrire. Paris. Abel L'Angelier (1586). Section 343, (1)ff, "Separated illustrations". Based on Bellaso, 1553.

Links

Nathaniel Johnston, Rows 1..26, flattened (full sequence)

Example

The array begins:
  1  2  3  4  5  6  7  8  9 10 ...
  2  3  4  5  6  7  8  9 10 11
  3  4  5  6  7  8  9 10 11 12
  4  5  6  7  8  9 10 11 12 13
  5  6  7  8  9 10 11 12 13 14
  6  7  8  9 10 11 12 13 14 15
  7  8  9 10 11 12 13 14 15 16
  8  9 10 11 12 13 14 15 16 17
  ...

Maple

for n from 1 to 26 do seq(1 + ((n+m-2) mod 26), m=1..26); od; # Nathaniel Johnston, Jun 23 2011

Mathematica

Flatten[Table[1+Mod[n+m-2, 26], {n, 10}, {m, 26}]] (* Harvey P. Dale, Feb 05 2012 *)

Crossrefs

Sequence in context: A295886 A318893 A338497 * A308702 A326200 A094759

Adjacent sequences: A137314 A137315 A137316 * A137318 A137319 A137320

Keyword

nonn,tabf,less,fini,full,word

Author

Paul Curtz, Apr 06 2008

Extensions

Edited by R. J. Mathar, Aug 06 2008

Status

approved