A087232 a(n) is the largest odd term in the 3x+1 trajectory initiated at n.

1, 1, 5, 1, 5, 5, 17, 1, 17, 5, 17, 5, 13, 17, 53, 1, 17, 17, 29, 5, 21, 17, 53, 5, 29, 13, 3077, 17, 29, 53, 3077, 1, 33, 17, 53, 17, 37, 29, 101, 5, 3077, 21, 65, 17, 45, 53, 3077, 5, 49, 29, 77, 13, 53, 3077, 3077, 17, 65, 29, 101, 53, 61, 3077, 3077, 1, 65, 33, 101, 17, 69

Offset: 1

Author

Labos Elemer, Sep 18 2003

Keywords

• nonn

Comments

a(n)=3077 corresponds to peak=9232.

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A025586, A056959, A348006.

Programs

Maple

a:= proc(n) option remember; `if`(n=1, 1, max(
     `if`(n::odd, n, 0), a(`if`(n::even, n/2, 3*n+1))))
    end:
seq(a(n), n=1..88);  # Alois P. Heinz, Nov 14 2021

Mathematica

c[x_] := (1-Mod[x, 2])*(x/2)+Mod[x, 2]*(3*x+1); c[1]=1; fpl[x_] := Delete[FixedPointList[c, x], -1] ofp[x_] := Part[fpl[x], Flatten[Position[OddQ[fpl[x]], True]]] Table[Max[ofp[w]], {w, 1, 256}]
(* Second program: *)
Array[Max@ Select[NestWhileList[If[EvenQ@ #, #/2, 3 # + 1] &, #, Unequal[#, 1, -1, -10, -34] &, 1, 10^4], OddQ] &, 69] (* Michael De Vlieger, May 15 2017, after Alonso del Arte at A025586 *)

Formula

If n = 2^k (for integers k >= 0), a(n) = 1; otherwise a(n) = (A025586(n)-1)/3 =(A056959(n)-1)/3. - Paolo Xausa, Nov 13 2021

Extensions

Name simplified by Paolo Xausa, Nov 13 2021