A083557 a(n) is the greatest prime factor of 3*a(n-1)+2.

3, 11, 7, 23, 71, 43, 131, 79, 239, 719, 127, 383, 1151, 691, 83, 251, 151, 13, 41, 5, 17, 53, 23, 71, 43, 131, 79, 239, 719, 127, 383, 1151, 691, 83, 251, 151, 13, 41, 5, 17, 53, 23, 71, 43, 131, 79, 239, 719, 127, 383, 1151, 691, 83, 251, 151, 13, 41, 5, 17, 53, 23

Offset: 1

Author

Yasutoshi Kohmoto, Jun 05 2003

Keywords

• nonn

Comments

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

Conjecture verified up to 25000000 by Jud McCranie, Jun 11 2003

Crossrefs

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

Programs

Mathematica

f[n_] := Flatten[Table[ #[[1]], {1}] & /@ FactorInteger[ 3n + 2 ]][[ -1]]; NestWhileList[f, 3, UnsameQ, All]
NestList[FactorInteger[3#+2][[-1,1]]&,3,70] (* Harvey P. Dale, Feb 21 2013 *)

PARI

lista(nn) = {print1(a = 3, ", "); for (n=1, nn, a = vecmax(factor(3*a+2)[,1]); print1(a, ", "););} \\ Michel Marcus, Jul 15 2017

Formula

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