# [seqfan] Re: (a+b) divides the concatenation [a,b]

Maximilian Hasler maximilian.hasler at gmail.com
Tue Sep 21 18:47:56 CEST 2010

```strictly increasing :

last=0;for(n=1,1e5, eval(Str(last,n))%(last+n)  | print1(last=n,","))
1,2,4,5,10,12,15,18,36,45,54,108,114,219,438,561,660,672,840,
1008,1071,1656,1677,2184,2260,2285,2742,3924,4257,5544,6677,
13354,13475,14938,18395,34450,37365,49350,50649,

yet unused :

used=last=0;for(n=1,1e4, bittest(used,n)&next;
eval(Str(last,n))%(last+n) &next; print1(last=n,","); used+=1<<n; n=0)

1,2,4,5,10,8,14,7,26,13,20,16,17,34,32,12,6,3,24,30,15,18,9,72,27,54,45,36,63,126,28,35,42,21,56,43,86,136,51,48,40,50,25,74,37,62,
31,68,64,80,19,38,61,122,76,23,46,53,106,92,115,218,109,224,84,70,29,58,41,82,140,91,52,47,94,128,160,60,39,78,65,120,96,192,104,112,
110,11,22,44,55,66,33,88,134,67,266,133,98,49,210,87,174,159,318,348,435,564,102,85,100,125,208,143,154,77,182,151,302,364,117,216,
81,162,171,342,144,152,57,114,95,190,180,90,75,150,183,366,300,105,228,69,138,195,156,168,165,132,201,402,264,99,198,135,108,225,330,
336,231,176,121,212,232,101,202,131,262,404,505,494,172,161,322,196,137,274,392,385,170,163,326,340,119,214,107,226,113,220,187,146,
73,260,130,203,406,116,145,188,235,320,124,155,178,89,244,200,250,305,610,389,778,221,238,280,164,169,312,354,177,822,411,588,189,
378,288,304,209,418,248,93,186,147,294,273,504,252,234,247,456,432,297,594,405,324,648,240,204,129,258,408,480,384,282,141,858,363,
528,286,308,358,179,820,287,490,245,310,356,445,554,277,722,361,638,319,464,424,242,352,314,157,842,421,578,289,710,71,142,191,382,284,
355,644,184,149,298,368,253,506,345,276,390,420,246,123,876,438,219,780,552,299,598,401,802,197,394,272,357,642,321,678,339,660,450,

Maximilian

On Tue, Sep 21, 2010 at 10:20 AM, Eric Angelini <Eric.Angelini at kntv.be> wrote:
>
>
>> Dropping the monotonically increasing
>> constraint would give V -- which I haven't
>> looked at yet.
>
> ... I hope I didn't make my usual mistake too
>    soon:
>
> V = 1,2,4,5,10,8,14,7,26,13,20,16,17,34,32,12,6,3,30,15,18,9,
>    24,42,21,56,28,35,64,68,31,62,37,74,25,50,40,48,51,102,...
>
> Rule:
> « Smallest integer not yet present in V such
>  that [a(n)+a(n+1)] divides the concatenation
>  of [a(n),a(n+1)] »
>
> Example here:
>
> 1+2 divides 12    ->  12/3=4
> 2+4 divides 24    ->  24/6=4
> 4+5 divides 45    ->  45/9=5
> 5+10 divides 510  -> 510/15=34
> 10+8 divides 108  -> 108/18=6
> 8+14 divides 814  -> 814/22=37
> ...
> Best,
> É.
>
>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>

```