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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". 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 (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 Table of n, a(n) for n=1..121. 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: A178094 A364874 A122556 * A084346 A165911 A354764 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 May 21 14:18 EDT 2024. Contains 372738 sequences. (Running on oeis4.)