[seqfan] Re: How many terms?

[Lars Blomberg]

For up to 8 digit start numbers I find no longer sequence than Jack Brennens:
46: 123,124,125,126,132,134,135,136,137,138,139,142,143,146,147,148,152,153,156,157,162,163,164,168,174,175,176,182,183,184,185,186,192,193,194,195,196,197,198,207,214,215,216,217,218,219

The longest starting with 1 is
33: 1,2,4,8,16,17,24,26,32,35,38,41,45,49,53,56,61,62,64,68,74,78,85,93,96,102,103,104,105,106,107,108,109

And the longest starting with 3 is
35: 3,6,12,13,14,15,16,17,24,26,32,35,38,41,45,49,53,56,61,62,64,68,74,78,85,93,96,102,103,104,105,106,107,108,109

/Lars

-----Ursprungligt meddelande-----
Från: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] För Jack Brennen
Skickat: den 8 december 2014 11:36
Till: seqfan at list.seqfan.eu; franktaw at netscape.net; Eric.Angelini at kntv.be
Ämne: [seqfan] Re: How many terms?

Best I have found with a quick C program is 46 terms.  The first such sequence lexicographically is:

123 124 125 126 127 134 135 136 137 138 139 142 143 146 147 148 149 153
156 157 158 159 164 168 169 175 176 182 183 184 185 186 192 193 194 195
196 197 198 207 214 215 216 217 218 219



   Jack

On 12/8/2014 9:46 AM, Frank Adams-Watters wrote:
> 3,6,12,13,14,15,16,... goes 30.
>
> Franklin T. Adams-Watters
>
> -----Original Message-----
> From: Eric Angelini <Eric.Angelini at kntv.be>
> To: Sequence Discussion list <seqfan at list.seqfan.eu>
> Sent: Mon, Dec 8, 2014 3:02 am
> Subject: [seqfan] How many terms?
>
>
>
> Hello SeqFans,
> How many terms could the longest such sequence S contain?
> 1) No term of S has a repeated digit (ex. 232 is forbidden)
> 2) a(n+1)=a(n)+[one digit of a(n)]
> 3) a(n+1)>a(n)
>
> This S has 28 terms, for instance, and is impossible to extend:
>
> S=1,2,4,8,16,17,18,19,28,36,39,42,46,52,54,58,63,69,75,82,84,92,94,98,
> 106
> ,107,108,109.
>
> Start S' with any integer and try to beat 28.
> Best,
> É.
>
>
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