%I #14 Jul 15 2017 11:26:38

%S 3,11,7,23,71,43,131,79,239,719,127,383,1151,691,83,251,151,13,41,5,

%T 17,53,23,71,43,131,79,239,719,127,383,1151,691,83,251,151,13,41,5,17,

%U 53,23,71,43,131,79,239,719,127,383,1151,691,83,251,151,13,41,5,17,53,23

%N a(n) is the greatest prime factor of 3*a(n-1)+2.

%C Conjecture: if a(1)=m then the sequence becomes cyclic, for any m.

%C Conjecture verified up to 25000000 by _Jud McCranie_, Jun 11 2003

%F G.f.: x*(3 + 11*x + 7*x^2 + 23*x^3 + 71*x^4 + 43*x^5 + 131*x^6 + 79*x^7 + 239*x^8 + 719*x^9 + 127*x^10 + 383*x^11 + 1151*x^12 + 691*x^13 + 83*x^14 + 251*x^15 + 151*x^16 + 13*x^17 + 41*x^18 + 2*x^19 + 6*x^20 + 46*x^21) / (1 - x^19) (conjectured). - _Colin Barker_, Jul 15 2017

%t f[n_] := Flatten[Table[ #[[1]], {1}] & /@ FactorInteger[ 3n + 2 ]][[ -1]]; NestWhileList[f, 3, UnsameQ, All]

%t NestList[FactorInteger[3#+2][[-1,1]]&,3,70] (* _Harvey P. Dale_, Feb 21 2013 *)

%o (PARI) lista(nn) = {print1(a = 3, ", "); for (n=1, nn, a = vecmax(factor(3*a+2)[,1]); print1(a, ", "););} \\ _Michel Marcus_, Jul 15 2017

%Y Cf. A031439, A031440, A031442, A082021, A082132, A084923.

%K nonn

%O 1,1

%A _Yasutoshi Kohmoto_, Jun 05 2003