# [seqfan] Re: S and S complementary : cumulative sum is prime accordingly

Douglas McNeil mcneil at hku.hk
Tue Jun 29 15:32:22 CEST 2010

```E. Angelini wrote:

>  S = 1, 4, 6, 7, 11, 13, 14, 15, 18, 20, 21, 27, 28, 29, 30, 33, 34, ...
> Scomp = 2, 3, 5, 8, 9, 10, 12, 16, 17, 19, 22, 23, 24, 25, 26, 31, 32, ...

I think I can confirm these terms -- it's harder to work backward from
an example than forward from a definition or rule -- but I'm not
convinced the sequence is uniquely specified, unless we select the
lexically first solution.  Don't most of these self-describing
attached?

sage: S[:100]
[1, 4, 6, 7, 11, 13, 14, 15, 18, 20, 21, 27, 28, 29, 30, 33, 34, 35,
37, 39, 40, 41, 44, 46, 48, 50, 51, 52, 53, 54, 66, 72, 73, 74, 75,
100, 101, 105, 106, 107, 108, 109, 114, 115, 121, 122, 124, 125, 133,
134, 135, 136, 137, 138, 140, 150, 168, 170, 178, 180, 186, 200, 204,
216, 234, 235, 237, 240, 252, 258, 260, 261, 262, 263, 265, 273, 278,
282, 286, 288, 290, 292, 312, 318, 338, 346, 350, 354, 360, 364, 366,
380, 396, 406, 410, 414, 426, 438, 462, 463]

Doug

--
Department of Earth Sciences
University of Hong Kong

```