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Search: id:A117754
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| A117754 |
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Triangular array based on addition of A034386 and A117682, and the factorial function modulo the factorial function. |
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+0
1
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| 0, 0, 0, 1, 1, 0, 2, 2, 3, 2, 7, 7, 8, 7, 12, 1, 1, 2, 1, 6, 0, 25, 25, 26, 25, 30, 144, 48, 211, 211, 212, 211, 216, 330, 234, 420, 1, 1, 2, 1, 6, 120, 24, 210, 0, 1729, 1729, 1730, 1729, 1734, 1848, 1752, 1938, 42048, 3456, 211, 211, 212, 211, 216, 330, 234, 420, 40530
(list; graph; listen)
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OFFSET
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0,7
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COMMENT
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This triangular array is organized like a group addition table.
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FORMULA
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f[n_, 1] = cf[n]; f[n_, 2] = p[n]; f[n_, 3] = n!; a(n,m) = Mod[f[n, 1 + Mod[n, 3]]+f[m, 1 + Mod[m, 3]], n! ]
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EXAMPLE
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0
0, 0
1, 1, 0
2, 2, 3, 2
7, 7, 8, 7, 12
1, 1, 2, 1, 6, 0
25, 25, 26, 25, 30, 144, 48
211, 211, 212, 211, 216, 330, 234, 420
1, 1, 2, 1, 6, 120, 24, 210, 0
1729, 1729, 1730, 1729, 1734, 1848, 1752, 1938, 42048, 3456
211, 211, 212, 211, 216, 330, 234, 420, 40530, 1938, 420
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MATHEMATICA
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Clear[f, g, cf, p, a, b] f[n_] := If[PrimeQ[n] == True, 1, n] cf[0] = 1; cf[n_Integer?Positive] := cf[n] = f[n]*cf[n - 1] g[n_] := If[PrimeQ[n] == True, n, 1] p[0] = 1; p[n_Integer?Positive] := p[n] = g[n]*p[n - 1] f[n_, 1] = cf[n]; f[n_, 2] = p[n]; f[n_, 3] = n!; a = Table[Table[Mod[f[n, 1 + Mod[n, 3]]+f[m, 1 + Mod[m, 3]], n! ], {m, 0, n}], {n, 0, 10}] Flatten[a]
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CROSSREFS
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Cf. A034386 and A117682.
Sequence in context: A092976 A084705 A141652 this_sequence A015999 A016001 A016012
Adjacent sequences: A117751 A117752 A117753 this_sequence A117755 A117756 A117757
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KEYWORD
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nonn,uned,probation
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AUTHOR
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Roger Bagula (rlbagulatftn(AT)yahoo.com), Apr 14 2006
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