# [seqfan] Re: Digitsum of a(n) is visible in a(n+1)

Charles Greathouse charles.greathouse at case.edu
Mon Feb 22 16:06:53 CET 2010

```110 < 111, so the sequence is more like

S = 1, 10, 11, 2, 12, 3, 13, 4, 14, 5, 15, 6, 16, 7, 17, 8, 18, 9, 19,
100, 21, 23, 25, 27, 29, 110, 20, 22, 24, 26, 28, 101, 32, 35, 38,
111, 30, 31, 34, 37, 102, 33, 36, 39, 112, 40, 41, 45, 49, 113, 50,
51, 46, 103, 42, 56, 114, 60, 61, 47, 115, 57, 120, 43, 67, 130, 44,
48, 121, 54, 59, 140, 52, 70, 71, 58, 131, 53, 68, 141, 62, 78, 150,
63, 69, 151, 72, 79, 116, 80, 81, 89, 117, 90, 91, 104, 55, 105, 64,
106, 73, 107, 82, 108, 92, 118, 109, 210, 83, 119, 211, 74, 311, 65,
411, 66, 122, 75, 123, 76, 132, 86, 142, 77, 143, 84, 124, 87, 152,
85, 133, 97, 160, 127, 310, 94, 134, 88, 161, 98, 170, 128, 511, 137,
611, 138, 125, 148, 135, 93, 126, 95, 144, 96, 153, 99, 180, 129, 212,
145, 410, 154, 510, 136, 610, 147, 312, 146, 711, 139, 213, 156, 412,
157, 313, 167, 149, 214, 171, 159, 155, 811, 710, 158, 314, 168, 215,
178, 162, 169, 163, 810, 179, 172, 910, 1000, 164, 911, 1011, 173,
1100, 182, 1101, 183, 512, 181, 1001, 192, 612, 189, 184, 413, 185,
414, 190, 1002, 193, 513, 191, 1102, 174, 712, 1003, 194, 514, 1004,
165, 812, 1103, 175, 613, 1005, 166, 713, 1104, 176, 614, 1105, 177,
315, 195, 415, 1006, 187, 216, 196, 316, 1007, 186, 515, 1106, ...

Charles Greathouse
Analyst/Programmer
Case Western Reserve University

On Mon, Feb 22, 2010 at 9:37 AM, Eric Angelini <Eric.Angelini at kntv.be> wrote:
>
> Hello SeqFans,
> here is another re-ordering of the Naturals:
>
> The digitsum of a(n) is visible in the smallest
> a(n+1) not yet present in S:
>
> S=1,10,11,2,12,3,13,4,14,5,15,6,16,7,17,8,18,
>  9,19,100,21,23,25,27,29,111,30,31,24,26,28,
>  101,20,22,34,37,102,32,35,38,112,40,41,45,
>  49,113,50,51,46,103,...
>
> ... this is computed by hand -- and fun to do!
>
> ---
>
> The 'equivalent' seq. is much harder to write:
>
> "Digitsum of a(n) is visible in a(n-1)", or (bet-
> ter), "a(n) shows the digitsum of the smallest
> a(n+1) not yet present in T":
>
> T=1,10,19,9,18,8,17,7,16,6,15,5,14,4,13,3,12,2,
>  11,29,20,101,28,26,24,22,110,37,21,...
>
> More headaches than fun with this one!
> Best,
> É.
>
>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>

```