A178174 a(1)=a(2)=a(3)=a(4)=1; thereafter a(n) = gpf(a(n-1)+a(n-2)+a(n-3)+a(n-4)), where gpf is the greatest prime factor.

1, 1, 1, 1, 2, 5, 3, 11, 7, 13, 17, 3, 5, 19, 11, 19, 3, 13, 23, 29, 17, 41, 11, 7, 19, 13, 5, 11, 3, 2, 7, 23, 7, 13, 5, 3, 7, 7, 11, 7, 2, 3, 23, 7, 7, 5, 7, 13, 2, 3, 5, 23, 11, 7, 23, 2, 43, 5, 73, 41, 3, 61, 89, 97, 5, 7, 11, 5, 7, 5, 7, 3, 11, 13, 17, 11, 13, 3, 11, 19, 23, 7, 5, 3, 19, 17, 11, 5, 13, 23, 13, 3, 13, 13, 7, 3, 3, 13, 13, 2, 31, 59, 7, 11, 3, 5, 13, 2, 23, 43, 3, 71, 7, 31

Offset: 1

Author

N. J. A. Sloane, Dec 18 2010

Keywords

• nonn
• easy

Comments

After 133 steps, enters a cycle of length 14.

Links

• Greg Back and Mihai Caragiu, The Greatest Prime Factor and Recurrent Sequences, Fibonacci Quart. 48 (2010), no. 4, 358-362.

Crossrefs

Cf. A006530, A175723, A177904.

Programs

Mathematica

nxt[{a_,b_,c_,d_}]:={b,c,d,FactorInteger[a+b+c+d][[-1,1]]}; Transpose[ NestList[ nxt,{1,1,1,1},120]][[1]] (* Harvey P. Dale, Sep 24 2013 *)