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, 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

Offset

0,12

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.

Links

Table of n, a(n) for n=0..54.

Formula

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

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

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]

Crossrefs

Sequence in context: A277144 A069848 A194702 * A198393 A083054 A336921

Adjacent sequences: A118679 A118680 A118681 * A118683 A118684 A118685

Keyword

nonn,tabl,base

Author

Roger L. Bagula, May 19 2006

Extensions

Edited by Franklin T. Adams-Watters, Sep 30 2011

Status

approved