# [seqfan] Re: Sequence A175252

hv at crypt.org hv at crypt.org
Mon Oct 10 00:34:05 CEST 2022

```Note that the related sequence A357273 is a superset with a slightly
looser condition: n is required to be a prefix of the concatenation
of the ordered divisors, but the prefix does not have to end on a
boundary between divisors.

A fairly simplistic search finds no example of either starting 17 with
up to 10 digits.

It may be easier to consider the binary sequence first: the prefix
version (not in OEIS, analogous to A357273) is shown, with asterisks
on those that also match whole divisors (A357428, analogous to A175252):

1 1 * 1
3 11
6 110 * 1, 2
7 111
15 1111
31 11111
52 110100 * 1, 2, 4
63 111111 * 1, 3, 7
127 1111111
222 11011110 * 1, 2, 3, 6
243 11110011
497 111110001
2037 11111110101 * 1, 3, 7, 21
3909 111101000101
6776 1101001111000 * 1, 2, 4, 7, 8
7122 1101111010010
8191 1111111111111
26896 110100100010000 * 1, 2, 4, 8, 16
32627 111111101110011
124641 11110011011100001 * 1, 3, 9, 11, 33
131071 11111111111111111
419669 1100110011101010101
524287 1111111111111111111

Hugo

Allan Wechsler <acwacw at gmail.com> wrote:
:I usually don't like "digit" questions, but this is a really cool one. I
:have only thought about it for about five minutes, but it seems like there
:is a lot going on here. It seems vaguely possible that a solution starting,
:say, 17, might be "engineered".
:
:On Wed, Oct 5, 2022 at 3:14 PM Michel Marcus <michel.marcus183 at gmail.com>
:wrote:
:
:> All terms of A175252 begin with digit 1.
:> All known terms begin with 12, 13 or 15.
:> Is it possible to find a term that begins with 11,14,16,17,18,19 ?
:>
:> Cheers.
:> MM
:>
:> --
:> Seqfan Mailing list - http://list.seqfan.eu/
:>
:
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:Seqfan Mailing list - http://list.seqfan.eu/

```