mod 6

[y.kohmoto]

    I tried to post a sequence that
    a(n) is the largest prime factor of sigma(a(n-1)^2).
    but it existed already on O.E..I.: A056650.

    I understood the reason why such a unpopular sequence existed.
    He extended A031439 which I posted

    By the way, I think his observation is interesting..

    And I searched for cases of several polynomial such that x^2+1, x^2-1,
x^2+2, x^+x+2, but I found no law except the case x^2-x+1.

    a(n) is the largest prime factor of a(n-1)^2-a(n-1)+1 :
         2,3,7,43,139,19183,2766679,        ----- I am going to post thie
sequecce to O.E.I.
         5,7,
         11,37,43,
         13,157,1289,3499,45289,

    It seems that the same law as A056650 exists.
    "Except the first term all terms are 1 mod 6."

    I don't have any idea to prove this proposition.
    Is it possible to prove it?

    Yasutoshi