A337349 To get a(n), take 3*n+1 and divide out any power of 2; then multiply by 3, subtract 1 and divide out any power of 2.

1, 1, 5, 7, 19, 1, 7, 1, 37, 5, 23, 25, 55, 7, 1, 17, 73, 19, 41, 43, 91, 1, 25, 13, 109, 7, 59, 61, 127, 1, 17, 35, 145, 37, 77, 79, 163, 5, 43, 11, 181, 23, 95, 97, 199, 25, 13, 53, 217, 55, 113, 115, 235, 7, 61, 31, 253, 1, 131, 133, 271, 17, 35, 71, 289, 73, 149

Offset: 0

Author

N. J. A. Sloane, based on email from Dan Asimov (dasimov(AT)earthlink.net), Sep 15 2006

Keywords

• nonn
• easy

Comments

When a(x) is iterated, what are the limit cycles? Are there any besides (1) and (17 -> 19 -> 43 -> 97 -> 109 -> 61)?

Up to 1000000000 every number eventually reaches one of those two cycles. In this range, the longest trajectory starts with n=458788881 and takes 193 steps to reach 1. - Christian Boyer (cboyer(AT)club-internet.fr), Sep 16 2006

Links

• Hugo Pfoertner, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A102421 (bisection), A102423.

Programs

Maple

A337349 := proc(n)
    local a;
    a := 3*n+1;
    while modp(a,2) = 0 do
        a := a/2 ;
    end do:
    a := 3*a-1 ;
    while modp(a,2) = 0 do
        a := a/2 ;
    end do:
    a ;
end proc: # R. J. Mathar, Aug 24 2020

Mathematica

a[n_] := Module[{k = 3n+1}, k = k/2^IntegerExponent[k, 2]; k = 3k-1; k = k/2^IntegerExponent[k, 2]; k];
a /@ Range[0, 100] (* Jean-François Alcover, Aug 27 2020 *)

Formula

a(n) = A075677(A067745(n+1)).

a(2*n+1) = A102421(n).