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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. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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

FORMULA

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

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

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-Fran├žois Alcover, Aug 27 2020 *)

CROSSREFS

Cf. A102421 (bisection), A102423.

Sequence in context: A153192 A263878 A297937 * A028319 A116640 A116623

Adjacent sequences:  A337346 A337347 A337348 * A337350 A337351 A337352

KEYWORD

nonn,easy

AUTHOR

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

STATUS

approved

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Last modified October 22 01:48 EDT 2021. Contains 348160 sequences. (Running on oeis4.)