A177923 a(1)=19, a(2)=13, a(3)=37; thereafter a(n) = gpf(a(n-1)+a(n-2)+a(n-3)), where gpf = "greatest prime factor".

19, 13, 37, 23, 73, 19, 23, 23, 13, 59, 19, 13, 13, 5, 31, 7, 43, 3, 53, 11, 67, 131, 19, 31, 181, 11, 223, 83, 317, 89, 163, 569, 821, 1553, 109, 191, 109, 409, 709, 409, 509, 1627, 509, 23, 127, 659, 809, 29, 499, 191, 719, 1409, 773, 967, 67, 139, 23, 229, 23, 11, 263, 11, 19, 293, 19, 331, 643, 331, 29, 59, 419, 13, 491, 71, 23, 13, 107, 13, 19, 139, 19, 59, 31, 109, 199, 113, 421, 733, 181, 89, 59, 47, 13, 17, 11, 41, 23, 5, 23, 17, 5, 5, 3, 13, 7, 23, 43, 73, 139, 17, 229, 11, 257, 71, 113, 7, 191, 311, 509, 337

Offset: 1

Author

N. J. A. Sloane, Dec 18 2010

Keywords

• nonn

Comments

This is the periodic part of A177904 - it is periodic with period 212.

A smaller start is a(1)=3, a(2)=13, a(3)=7, but that would not produce the terms in the order of their first appearance in A177904.

There are several open questions concerning this class of sequences - see the Back-Caragiu reference in A177904.

Links

• N. J. A. Sloane, Table of n, a(n) for n = 1..212

Crossrefs

Cf. A006530, A177904, A175723.

Programs

Mathematica

nxt[{a_,b_,c_}]:={b,c,FactorInteger[a+b+c][[-1,1]]}; NestList[nxt,{19,13,37},120][[All,1]] (* Harvey P. Dale, Dec 11 2018 *)