

A175723


a(1)=a(2)=1; thereafter a(n) = gpf(a(n1)+a(n2)), where gpf = "greatest prime factor".


19



1, 1, 2, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5, 2, 7, 3, 5
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OFFSET

1,3


COMMENTS

Rapidly enters a loop with period 3,5,2,7.
More generally, if a(1) and a(2) are distinct positive numbers with a(1)+a(2) >= 2, the sequence eventually enters the cycle {7,3,5,2} [Back and Caragiu].


LINKS



MATHEMATICA

nxt[{a_, b_}]:={b, FactorInteger[a+b][[1, 1]]}; Transpose[NestList[nxt, {1, 1}, 120]][[1]] (* or *) PadRight[{1, 1, 2}, 130, {5, 2, 7, 3}] (* Harvey P. Dale, Feb 24 2015 *)


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



