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

1,4

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))
-- Reinhard Zumkeller, Jul 24 2012

Crossrefs

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

Sequence in context: A345014 A328878 A178095 * A049072 A059887 A023585

Adjacent sequences: A177901 A177902 A177903 * A177905 A177906 A177907

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 16 2010

Status

approved