[seqfan] Prime is not random

[zbi74583.boat at orange.zero.jp]

    Hi  Seqfans

    a(n)=Prime(n)+Prime(n+M_3(Prime(n)))  Mod 4
    Where if m=1 Mod 3 then M_3(m)=-1
              if m=2 Mod 3 then M_3(m)= 1

    a(n) : 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
    If Prime(n) and Prime(n+1) are twin then a(n)=0 and a(n+1)=0
    I think it represents the Non Randomness of Prime
    Because if Prime behaves randomly then the probability of 0 and 2 must be
the same

    b(n)=Prime(n)+Prime(n-M_3(Prime(n)))  Mod 4
    b(n) : 0, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2,
2

    Could anyone compute more term  ?



    Yasutoshi