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

Offset: 1

Author

N. J. A. Sloane, Dec 16 2010

Keywords

• nonn
• easy

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.

Crossrefs

Cf. A006530, A175723, A178174, A178095, A214320.

Programs

Haskell

a177904 n = a177904_list !! (n-1)
a177904_list = 1 : 1 : 1 : (map a006530 $ zipWith (+)
   a177904_list (tail $ zipWith (+) a177904_list $ tail a177904_list))
-- Reinhard Zumkeller, Jul 24 2012

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 *)