

A121809


Primes modulo five partitioned sequentially in groups of four are then given the number of the order in which such groupings come up sequentially in an n X n X n X n vector.


0



74, 237, 74, 178, 47, 211, 122, 32, 26, 177, 157, 159, 194, 178, 42, 37, 95, 220, 181, 241, 188, 74, 212, 179, 23, 198, 178, 157, 39, 202, 132, 220, 133, 230, 195, 127, 122, 38, 62, 26, 25, 124, 12, 195, 211, 110, 179, 130, 138, 178, 248, 178, 40, 18, 144, 159
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OFFSET

1,1


COMMENTS

There are 256 ways you can get a onedimensional tile of colors {red, green, blue, yellow}: these are used to index the appearance of modulo five appearance of such orders in the primes. The most popular occurrence is {4,5,2,3} at 5 for the first 256 prime partitions after the prime 5.


LINKS



FORMULA

a0[m] = {1 + Mod[Prime[m], 5],1 + Mod[Prime[m+1], 5],1 + Mod[Prime[m+2], 5]1 + Mod[Prime[m+3], 5]} b0[n]={x[n],y[n],z[n],w[n]} a(m) = a0[m] indexed by b0[n].


EXAMPLE

a[[4]] > b[[178]] = {4, 5, 2, 3}.


MATHEMATICA

a = Partition[Table[1 + Mod[Prime[n], 5], {n, 4, 260}], 4]; b = Union[Flatten[Table[{x, y, z, t}, {x, 2, 5}, {y, 2, 5}, {z, 2, 5}, {t, 2, 5}], 3]]; f[n_, m_] := If[a[[m]]  b[[n]] == {0, 0, 0, 0}, n, {}] c=Flatten[Table[f[m, n], {n, Length[a]}, {m, Length[b]}]]


CROSSREFS



KEYWORD

nonn,uned


AUTHOR



STATUS

approved



