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 A175723 a(1)=a(2)=1; thereafter a(n) = gpf(a(n-1)+a(n-2)), where gpf = "greatest prime factor". 18
 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 (list; graph; refs; listen; history; text; internal format)
 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 G. Back and M. Caragiu, The greatest prime factor and recurrent sequences, Fib. Q., 48 (2010), 358-362. 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 Cf. A000045, A006530, A020639. Similar or related sequences: A177904, A177923, A178094, A178095, A178174, A178179, A180101, A180107, A221183. Sequence in context: A073481 A178094 A122556 * A084346 A165911 A096062 Adjacent sequences:  A175720 A175721 A175722 * A175724 A175725 A175726 KEYWORD nonn AUTHOR N. J. A. Sloane, Dec 16 2010 STATUS approved

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Last modified December 19 03:45 EST 2018. Contains 318245 sequences. (Running on oeis4.)