[seqfan] Re: Sequence A175252
David Corneth
davidacorneth at gmail.com
Mon Oct 10 14:23:39 CEST 2022
Michel and I found some terms for A175252 by listing divisors of "small"
positive integers. Like listing the divisors of 693 and sticking them
together from left to right gives the term 13791121336377.
So maybe by checking the divisors of 7-rough numbers might give a term
starting with 17.
Best,
David
On Mon, Oct 10, 2022 at 1:05 AM <hv at crypt.org> wrote:
> 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
> :>
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> :>
> :
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