A214320 a(0)=a(1)=a(2)=1; thereafter a(n) = gpf(a(n-1)+a(n-3)), where gpf = "greatest prime factor".

1, 1, 1, 2, 3, 2, 2, 5, 7, 3, 2, 3, 3, 5, 2, 5, 5, 7, 3, 2, 3, 3, 5, 2, 5, 5, 7, 3, 2, 3, 3, 5, 2, 5, 5, 7, 3, 2, 3, 3, 5, 2, 5, 5, 7, 3, 2, 3, 3, 5, 2, 5, 5, 7, 3, 2, 3, 3, 5, 2, 5, 5, 7, 3, 2, 3, 3, 5, 2, 5, 5, 7, 3, 2, 3, 3, 5, 2, 5, 5, 7, 3, 2, 3, 3, 5, 2, 5, 5, 7, 3, 2, 3, 3, 5, 2, 5, 5, 7, 3, 2, 3, 3, 5, 2, 5, 5, 7, 3, 2, 3, 3, 5, 2, 5, 5, 7, 3, 2, 3, 3

Offset: 0

Author

N. J. A. Sloane, Jul 22 2012

Keywords

• nonn

Comments

Suggested by A214551 and A177904.

Crossrefs

Cf. A000930, A006530, A177904, A214320.

Programs

Haskell

a214320 n = a214320_list !! n
a214320_list = 1 : 1 : 1 : (map a006530 $
   zipWith (+) a214320_list (drop 2 $ a214320_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;
f:=proc(n) option remember; if n <= 2 then 1 else A006530(f(n-1)+f(n-3)); fi; end;
[seq(f(n),n=0..120)];

Mathematica

nxt[{a_,b_,c_}]:={b,c,FactorInteger[c+a][[-1,1]]}; NestList[nxt,{1,1,1},120][[All,1]] (* or *) PadRight[{1,1,1,2,3,2,2},130,{3,2,3,3,5,2,5,5,7}] (* Harvey P. Dale, Jul 08 2017 *)

Formula

After 7 terms, cycles with period 9.