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A137317
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Array T(n,m) = 1 + (n+m-2) mod 26, 1 <= n,m <= 26, read by rows or columns.
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2
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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
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OFFSET
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1,2
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COMMENTS
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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.).
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REFERENCES
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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.
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LINKS
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EXAMPLE
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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
...
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MAPLE
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for n from 1 to 26 do seq(1 + ((n+m-2) mod 26), m=1..26); od; # Nathaniel Johnston, Jun 23 2011
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MATHEMATICA
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Flatten[Table[1+Mod[n+m-2, 26], {n, 10}, {m, 26}]] (* Harvey P. Dale, Feb 05 2012 *)
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CROSSREFS
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KEYWORD
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nonn,tabf,less,fini,full,word
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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