A117339 a(n) = a(n-1) + a(n-2); if a(n) is not prime divide a(n) by its largest prime factor.

1, 1, 2, 3, 5, 4, 3, 7, 2, 3, 5, 4, 3, 7, 2, 3, 5, 4, 3, 7, 2, 3, 5, 4, 3, 7, 2, 3, 5, 4, 3, 7, 2, 3, 5, 4, 3, 7, 2, 3, 5, 4, 3, 7, 2, 3, 5, 4, 3, 7, 2, 3, 5, 4, 3, 7, 2, 3, 5, 4, 3, 7, 2, 3, 5, 4, 3, 7, 2, 3, 5, 4, 3, 7, 2, 3, 5, 4, 3, 7, 2, 3, 5, 4, 3, 7, 2, 3, 5, 4, 3, 7, 2, 3, 5, 4, 3, 7, 2, 3, 5, 4, 3, 7, 2

Offset: 1

Author

Zak Seidov, Mar 09 2006

Keywords

• nonn
• easy

Comments

Sequence repeats cyclically. Conjecture: sequence ends with cycle for any positive a(1) and a(2). This has been checked for a(1)=1 and a(2)=1,...,2000. Some other cases shown below: a(1), a(2), length of s, sequence s 1,1,10,{1,1,2,3,5,4,3,7,2,3}, 1,2,9,{1,2,3,5,4,3,7,2,3}, 1,3,9,{1,3,2,5,7,4,11,3,2}, 1,4,20,{1,4,5,3,4,7,11,6,17,23,8,31,3,2,5,7,4,11,3,2}, 1,5,12,{1,5,2,7,3,2,5,7,4,11,3,2}, 1,6,23,{1,6,7,13,4,17,3,4,7,11,6,17,23,8,31,3,2,5,7,4,11,3,2}, 1,7,9,{1,7,4,11,3,2,5,7,4}, 1,8,30,{1,8,3,11,2,13,3,8,11,19,6,5,11,8,19,9,4,13,17,6,23,29,4,3,7,2,3,5,4,3}, 1,9,34,{1,9,2,11,13,8,3,11,2,13,3,8,11,19,6,5,11,8,19,9,4,13,17,6,23,29,4,3,7,2,3,5,4,3}, 1,10,10,{1,10,11,3,2,5,7,4,11,3}. Even exotic seeds give no long sequences, e.g. 967,3000,24,{967,3000,3967,6967,154,7121,75,28,103,131,18,149,167,4,9,13,2,3,5,4,3,7,2,3}. For a(1)=1, maximal length = 55 is found for a(2)=1207: 1,1207,55,{1,1207,8,243,251,26,277,3,40,43,83,18,101,7,36,43,79,2,27,29,8,37,9,2,11,13,8,3,11,2,13,3,8,11,19,6,5,11,8,19,9,4,13,17,6,23,29,4,3,7,2,3,5,4,3}.

Links

• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,1).

Crossrefs

Cf. A214674.

Formula

G.f.: -(6*x^8+2*x^7+4*x^6+5*x^5+3*x^4+2*x^3+x^2+x)/(x^6-1). - Alois P. Heinz, Apr 20 2023