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

0,4

Comments

Suggested by A214551 and A177904.

Links

Table of n, a(n) for n=0..120.

Formula

After 7 terms, cycles with period 9.

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 *)

Prog

(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

Crossrefs

Cf. A000930, A006530, A177904, A214320.

Sequence in context: A318177 A128651 A093797 * A119809 A007653 A353623

Adjacent sequences: A214317 A214318 A214319 * A214321 A214322 A214323

Keyword

nonn

Author

N. J. A. Sloane, Jul 22 2012

Status

approved