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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 (list; graph; refs; listen; history; text; internal format)
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)club-internet.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*j-1; 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

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Last modified October 20 15:14 EDT 2017. Contains 293612 sequences.