# [seqfan] Re: Duplicates? A177729 A177517 A177516

franktaw at netscape.net franktaw at netscape.net
Fri May 14 13:30:09 CEST 2010

```Responses inline.

-----Original Message-----
From: Richard Mathar <mathar at strw.leidenuniv.nl>

What is the relation between these two:

http://oeis.org/classic/?q=id:A177729|id:A061641
1,2,3,6,7,9,12,15,18,19,21,24,25,27,30,33,36,37,39,42,43,45,48,51,54,55,5
7,60,63,66,69,72,73,75,78,79,81,84,87,90,93,96,97,99,102,105,108,109,111,
114,115,117,120,123,126,127,129,132,133,135,138,141,
0,1,3,6,7,9,12,15,18,19,21,24,25,27,30,33,36,37,39,42,43,45,48,51,54,55,5
7,60,63,66,69,72,73,75,78,79,81,84,87,90,93,96,97,99,102,105,108,109,111,
114,115,117,120,123,126,127,129,132,133,135,138,141,144,145,

<<<<<
>From the definitions, these should be the same.

The inclusion of 2 in A177729 is apparently due to a non-standard
definition of a Collatz sequence; A177729 assumes that the Collatz
sequence ends when it reaches 1, whereas the standard definition
includes the periodic 1,4,2,... from that point.

The inclusion of 0 in A061641 is a bit odd, but I won't say it's wrong.
One usually looks only at positive integers for Collatz sequences.

Incidentally, the (modified) conjecture in A177729 that no numbers == 2
(mod 3) are in the sequence is correct; starting with 2n+1, the next
two numbers are 6n+4 and then 3n+2.
>>>>>

or between these (pattern avoiding):

http://oeis.org/classic/?q=id:A177517|id:A177477
1,2,6,19,70,331,1863,11637,81110,635550,5495339,51590494,524043395,574354
6943,67478821537,844983073638,11240221721390,
1,2,6,19,70,331,1863,11637,81110,

<<<<<
These are defined identically.
>>>>>

http://oeis.org/classic/?q=id:A177516|id:A177479
1,2,6,21,90,450,2619,17334,129114,1067661,9713682,96393726,1036348587,119
98603710,148842430470,1969461102357,27688474234602,
1,2,6,21,90,450,2619,17334,129114,

<<<<<
A177479 avoids the pattern down, down, up, while A177479 avoids up,
down, down. Reversing the order of a pattern doesn't change the number
of permutations that avoid it, so these are the same. (Swapping up and
down will also leave the count unchanged.)
>>>>>

```