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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

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: A073481 A178094 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 September 27 15:39 EDT 2022. Contains 357062 sequences. (Running on oeis4.)