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A118682
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Triangle where T(n,k) depends on the last digit of prime(n)*prime(k). If this is 1 or 9, T(n,k) = 1; if 3 or 7, T(n,k) = 2; otherwise T(n,k) = 0.
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0
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0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 2, 1, 0, 1, 0, 1, 2, 1, 0, 1, 0, 1, 2, 1, 1, 0, 2, 0, 2, 1, 2, 2, 1, 0, 1, 0, 1, 2, 1, 1, 2, 1, 0, 2, 0, 2, 1, 2, 2, 1, 2, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,12
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COMMENTS
| Previous title: A triangular factor function based on the modulo 10 last digit multiplication behavior of the primes (modeled on Jacobi symbols and Legendre symbols).
T(n,k) = 0 exactly when one of the primes is 2 or 5.
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FORMULA
| T(n,k) = vector(0,1,0,2,0,0,0,2,0,1)[mod(prime(n)*prime(k),10)+1].
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EXAMPLE
| 0
0, 1
0, 0, 0
0, 1, 0, 1
0, 2, 0, 2, 1
0, 1, 0, 1, 2, 1
0, 1, 0, 1, 2, 1, 1
0, 2, 0, 2, 1, 2, 2, 1
0, 1, 0, 1, 2, 1, 1, 2, 1
0, 2, 0, 2, 1, 2, 2, 1, 2, 1
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MATHEMATICA
| f[n_, m_] = If[(Mod[Prime[n]*Prime[m], 10] - 1 == 0) || (Mod[Prime[n]*Prime[m], 10] - 9 == 0), 1, If[(Mod[Prime[n]*Prime[m], 10] - 3 == 0) || (Mod[Prime[n]*Prime[m], 10] - 7 == 0), 2, 0]] a = Table[Table[f[n, m], {n, 1, m}], {m, 1, 10}] aout = Flatten[a]
This function gives an op-art pattern from the primes as: bout = Table[f[n, m], {n, 1, 60}, {m, 1, 60}]; ListDensityPlot[bout, Mesh -> False]
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CROSSREFS
| Sequence in context: A072627 A069848 A194702 * A198393 A083054 A061264
Adjacent sequences: A118679 A118680 A118681 * A118683 A118684 A118685
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KEYWORD
| nonn,tabl,base
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), May 19 2006
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EXTENSIONS
| Edited by Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Sep 30 2011
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