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

1,1

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

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 *)

Crossrefs

Cf. A006530, A177904, A175723.

Sequence in context: A196188 A089294 A088934 * A155848 A088399 A106706

Adjacent sequences: A177920 A177921 A177922 * A177924 A177925 A177926

Keyword

nonn

Author

N. J. A. Sloane, Dec 18 2010

Status

approved