[seqfan] Prime is not random

zbi74583.boat at orange.zero.jp zbi74583.boat at orange.zero.jp
Thu May 12 04:33:30 CEST 2016


    Prime is not random
    For example see A103271

    The randomness of A103270  is much smaller than A103271

    Could anyone compute more terms?

    More non random sequence

    a(n)=Prime(n)+Prime(n-k) Mod 4, where k=1/2*(Prime(n)-Prime(n-1))
    a(n) : 0,0,0,0,0,0,0,2,0,0,0,0,0,2,2,0,0,0,0
    OFFSET  5

    Two random sequences whose formula look like A103270 and a(n)

    See A103272

    b(n)=Prime(n)+Prime(n+k) Mod 4, where k=1/2*(Prime(n)-Prime(n-1))
    b(n): 0,2,0,2,0,2,2,2,0,0,0,2,2,0,2,0,2,2,0
    OFFSET  5

    More non random sequences

    c(n)=Prime(m+k) Mod 4 , where Prime(m)=F(n) , k=1/2*(Prime(m+1)-Prime(m))
                            where F(n) is n-th Prime which is 1 Mod 4
    c(n): 3,3,3,3,3,3,3,1,1,3,3,3

    d(n)=Prime(m+k) Mod 4 , where Prime(m)=G(n) , k=1/2*(Prime(m+1)-Prime(m))
                            where G(n) is n-th Prime which is 3 Mod 4
    d(n): 1,1,1,1,1,3,1,1,1,1,1,1,1,1


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