# [seqfan] Re: Add (to me) my even biggest digit

Sun Oct 12 23:25:28 CEST 2014

```Certainly you can get sequences of arbitrary length. Start at 2 * 10^k
and you will get more than 10^(k-1) terms.

-----Original Message-----
From: Neil Fernandez <primeness at borve.org>

Hi all,

Eric.Angelini wrote:

>Ah, thank you Juan -- I'm pretty sure now
>that no such infinite seq is possible. At some point, it will halt.

All sequences starting with x < 100000 halt.

Lengths of sequences starting with 2,4,6,...,100 are

129, 128, 128, 127, 1, 127, 126, 126, 125, 126, 125, 124, 124, 123, 1,
123, 122, 122, 121, 9, 121, 8, 120, 7, 1, 119, 118, 6, 117, 117, 5, 2,
116, 4, 1, 115, 114, 3, 113, 113, 2, 113, 112, 112, 1, 112, 111, 111,
110, 1

Integers x < 100000 with sequences longer than for all smaller x are

2 (stops at 700, length 129)
580 (stops at 1700, length 198)
1580 (stops at 3700, length 378)
19580 (stops at 30700, length 1903)

Can we get sequences of arbitrary length?

Best regards,

Neil

--
Neil Fernandez

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