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A118682 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. 0

%I #6 Mar 30 2012 17:35:16

%S 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,

%T 2,1,0,1,0,1,2,1,1,2,1,0,2,0,2,1,2,2,1,2,1

%N 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.

%C 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).

%C T(n,k) = 0 exactly when one of the primes is 2 or 5.

%F T(n,k) = vector(0,1,0,2,0,0,0,2,0,1)[mod(prime(n)*prime(k),10)+1].

%e 0

%e 0, 1

%e 0, 0, 0

%e 0, 1, 0, 1

%e 0, 2, 0, 2, 1

%e 0, 1, 0, 1, 2, 1

%e 0, 1, 0, 1, 2, 1, 1

%e 0, 2, 0, 2, 1, 2, 2, 1

%e 0, 1, 0, 1, 2, 1, 1, 2, 1

%e 0, 2, 0, 2, 1, 2, 2, 1, 2, 1

%t 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]

%t 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]

%K nonn,tabl,base

%O 0,12

%A _Roger L. Bagula_, May 19 2006

%E Edited by _Franklin T. Adams-Watters_, Sep 30 2011

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Last modified March 29 07:27 EDT 2024. Contains 371265 sequences. (Running on oeis4.)