

A102421


Start with 2n+1, multiply by 3 and add 1 and divide out any power of 2; then multiply by 3 and subtract 1 and divide out any power of 2.


2



1, 7, 1, 1, 5, 25, 7, 17, 19, 43, 1, 13, 7, 61, 1, 35, 37, 79, 5, 11, 23, 97, 25, 53, 55, 115, 7, 31, 1, 133, 17, 71, 73, 151, 19, 5, 41, 169, 43, 89, 91, 187, 1, 49, 25, 205, 13, 107, 109, 223, 7, 29, 59, 241, 61, 125, 127, 259, 1, 67, 17, 277, 35, 143, 145, 295, 37, 19, 77, 313
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OFFSET

0,2


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)clubinternet.fr), Sep 16 2006


LINKS

Table of n, a(n) for n=0..69.


EXAMPLE

n=1, 2n+1 = 3 > 10 > 5; 5 > 14 >7 = a(1).


MAPLE

f:=proc(n) local j; j:=3*n+1; while j mod 2 = 0 do j:=j/2; od: j:=3*j1; while j mod 2 = 0 do j:=j/2; od: j; end;


MATHEMATICA

nextx[x_Integer] := Block[{ a = x}, a = 3a + 1; While[EvenQ@a, a /= 2]; a = 3a  1; While[EvenQ@a, a /= 2]; a]; Table[ nextx[2n + 1], {n, 0, 69}] (* Robert G. Wilson v Sep 20 2006 *)


CROSSREFS

Cf. A102423.
Sequence in context: A019980 A258986 A086384 * A019620 A105395 A120437
Adjacent sequences: A102418 A102419 A102420 * A102422 A102423 A102424


KEYWORD

nonn


AUTHOR

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


STATUS

approved



