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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
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
Similar or related sequences: A177904, A177923, A178094, A178095, A178174, A178179, A180101, A180107, A221183.
Sequence in context: A178094 A364874 A122556 * A084346 A165911 A354764
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.)