Voozh

A177904

a(1)=a(2)=a(3)=1; thereafter a(n) = gpf(a(n-1)+a(n-2)+a(n-3)), where gpf = "greatest prime factor".

1, 1, 1, 3, 5, 3, 11, 19, 11, 41, 71, 41, 17, 43, 101, 23, 167, 97, 41, 61, 199, 43, 101, 7, 151, 37, 13, 67, 13, 31, 37, 3, 71, 37, 37, 29, 103, 13, 29, 29, 71, 43, 13, 127, 61, 67, 17, 29, 113, 53, 13, 179, 7, 199, 11, 31, 241, 283, 37, 17, 337, 23, 29, 389, 7, 17, 59, 83, 53, 13, 149, 43, 41, 233, 317, 197, 83, 199, 479, 761, 1439, 47, 107

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OFFSET

1,4

COMMENTS

After 86 steps, enters a cycle of length 212 (see A177923).

LINKS

N. J. A. Sloane, Table of n, a(n) for n = 1..1000

G. Back and M. Caragiu, The greatest prime factor and recurrent sequences, Fib. Q., 48 (2010), 358-362.

MAPLE

with(numtheory, divisors); A006530 := proc(n) local i, t1, t2, t3, t4, t5; t1 := divisors(n); t2 := convert(t1, list); t3 := sort(t2); t4 := nops(t3); t5 := 1; for i from 1 to t4 do if isprime(t3[t4+1-i]) then RETURN(t3[t4+1-i]); fi; od; 1; end;

M:=1000;

t1:=[1, 1, 1];

for n from 4 to M do

t1:=[op(t1), A006530(t1[n-1]+t1[n-2]+t1[n-3])]; od:

t1;

MATHEMATICA

nxt[{a_, b_, c_}]:={b, c, FactorInteger[a+b+c][[-1, 1]]}; NestList[nxt, {1, 1, 1}, 90][[All, 1]] (* Harvey P. Dale, Jul 17 2017 *)

PROG

(Haskell)

a177904 n = a177904_list !! (n-1)

a177904_list = 1 : 1 : 1 : (map a006530 $ zipWith (+)

a177904_list (tail $ zipWith (+) a177904_list $ tail a177904_list))