Self-Complementary Sieve

[pauldhanna at juno.com]

Joshua (and SeqFans), 
     You got it right - thanks! 
Please submit these sequences if you wish, 
with your examples and clarity. 
Good work. 
     Paul 
 
On Wed, 12 Mar 2008 22:41:23 -0700 "Joshua Zucker"
<joshua.zucker at gmail.com> writes:
[...]
> Hi Paul and seqfans,
> I think this is a cute idea, reminiscent of Hofstadter's
> 1,3,7,12,18,26 (A005228).  It feels like an interesting flavor of
> self-reference combined with Eratosthenes-ish sieving.
> 
> If I understand your definition correctly, which I may not, I get
> A138203: 1 3 5 9 11 17 21 27 33 37 43 51 59 69 81 91 97
> A138204: 2 4 6 7 8 10 12 13 14 15 16 18 19
> 
> Since we disagree at a pretty early term, it should be easy to figure
> out which one of us is confused.  Here's my process:
> delete every 2nd term: (1 3 5 7 9 11 13 15 17 19 21 23 25 27 29)
> 4 is missing, so delete every 4th term (7, 15, 23, etc.): 
> (1 3 5 9 11 13 17 19 21 25 27 29)
> 6 is missing, so delete every 6th term (13, 29): (1 3 5 9 11 17 19 21
25 27)
> 7 is missing, delete the 7th term (19): (1 3 5 9 11 17 21 25 27)
> 8 is missing, delete the 8th term (25): (1 3 5 9 11 17 21 27)
> now future deletions won't hit any of those terms, so those at least
> are guaranteed.  Since we already differ (you have 19 and I don't),
> please let me know if I've misunderstood your process!
> 
> Just in case I did get it right, here are more terms.
> For A138203, the first 205 terms gets us up to the last term under
10000:
> 1 3 5 9 11 17 21 27 33 37 43 51 59 69 81 91 97 105 117 133 137 149 169
> 181 195 211 213 235 259 273 297 307 313 339 361 369 403 409 435 465
> 481 485 515 539 565 581 627 641 665 689 707 739 755 785 821 853 873
> 913 917 963 993 1009 1051 1097 1121 1153 1173 1257 1259 1285 1301 1371
[...] 
> and for A138204, well, it'll just be the complement, so that's 
> simple
> enough.  But we only need to go up to 205 to guarantee the above
> sequence, so:
> 2 4 6 7 8 10 12 13 14 15 16 18 19 20 22 23 24 25 26 28 29 30 31 32 34
> 35 36 38 39 40 41 42 44 45 46 47 48 49 50 52 53 54 55 56 57 58 60 61
> 62 63 64 65 66 67 68 70 71 72 73 74 75 76 77 78 79 80 82 83 84 85 86
[...]
> --Joshua Zucker