

A175723


a(1)=a(2)=1; thereafter a(n) = gpf(a(n1)+a(n2)), 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
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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

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), 358362.


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



