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A106728
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Triangular array based on modulo ten addition of the primes under a modulo five, modulo four function.
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0
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2, 3, 0, 1, 2, 0, 2, 3, 1, 2, 0, 1, 3, 0, 2, 1, 2, 0, 1, 3, 0, 0, 1, 3, 0, 2, 3, 2, 3, 0, 2, 3, 1, 2, 1, 0, 2, 3, 1, 2, 0, 1, 0, 3, 2, 3, 0, 2, 3, 1, 2, 1, 0, 3, 0, 1, 2, 0, 1, 3, 0, 3, 2, 1, 2, 0, 2, 3, 1, 2, 0, 1, 0, 3, 2, 3, 1, 2, 1, 2, 0, 1, 3, 0, 3, 2, 1, 2, 0, 1, 0, 0, 1, 3, 0, 2, 3, 2, 1, 0, 1, 3, 0, 3, 2
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| The obect of these modulo functions is form a group under Addition. Triangular form: {2} {3, 0} {1, 2, 0} {2, 3, 1, 2} {0, 1, 3, 0, 2} {1, 2, 0, 1, 3, 0} {0, 1, 3, 0, 2, 3, 2} These can be translated back to modulo 10 by using the substitution: 0->9 1->1 2->7 3->3
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FORMULA
| f(n)=10-Mod[Prime[n+3], 10] g[n]=Mod[Mod[n, 5], 4] h(n)]=g(f(n)) a[n, m)=Mod[h[n)+h(m), 4]
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MATHEMATICA
| f[n_] = 10 - Mod[Prime[n + 3], 10] g[n_] = Mod[Mod[n, 5], 4] h[n_] = g[f[n]] digits = 20 a = Table[Table[Mod[h[n]+h[m], 4], {n, 1, m}], {m, 1, digits}]; MatrixForm[a] Flatten[a]
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CROSSREFS
| Sequence in context: A103498 A030386 A096799 * A189480 A010873 A049804
Adjacent sequences: A106725 A106726 A106727 * A106729 A106730 A106731
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KEYWORD
| nonn,uned
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), May 14 2005
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