[seqfan] Re: possible sequence

[franktaw at netscape.net]

That's what I started to say, but then I realized that it's the 
opposite condition of what we are trying to prove.

Franklin T. Adams-Watters

-----Original Message-----
From: Charles Greathouse <charles.greathouse at case.edu>
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
Sent: Fri, Mar 7, 2014 11:14 am
Subject: [seqfan] Re: possible sequence


I don't think it's workable, since the cycles mod 10^n must contain 2^n
which will have leading zeros for n > 1.

Charles Greathouse
Analyst/Programmer
Case Western Reserve University


On Fri, Mar 7, 2014 at 10:48 AM, <franktaw at netscape.net> wrote:

> If 2^86 is zero-free, with 26 digits, then the 26 digit cycle contains
> zero-free numbers. So this would have to be at least the 27-digit 
cycle.
>
> Franklin T. Adams-Watters
>
>
> -----Original Message-----
> From: Allan Wechsler <acwacw at gmail.com>
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Sent: Fri, Mar 7, 2014 8:35 am
> Subject: [seqfan] Re: possible sequence
>
>
> I can vaguely imagine proving an upper bound on A007377, since any 
fixed
> number of low-order digits of the powers of two must eventually enter 
a
> cycle.  If one could actually step through, say, the 15-digit cycle, 
and
> find that every step had a zero ...
>
>
> On Thu, Mar 6, 2014 at 9:06 PM, Charles Greathouse <
> charles.greathouse at case.edu> wrote:
>
>  2^86 (26 digits) is conjectured to be the last 0-free power of two,
>> see A007377.
>>
>> 2^184 * 3^88 (98 digits) seems to be the last 0-free 3-smooth number.
>>
>> 0-free numbers cannot contain both 2s and 5s, and the best {3,
>>
> 5}-smooth
>
>> number I can find is 3^28 * 5^90 (77 digits), so it looks like the
>>
> largest
>
>> 0-free 5-smooth number is 2^184 * 3^88 again.
>>
>> I don't know what the largest 0-free 7-smooth number is, but it's at
>> least 2^298 * 3^69 * 7^7 (129 digits).
>>
>> One problem is that this sequence grows very quickly. Another is that
>>
> no
>
>> terms are actually known...! But it is interesting to think about.
>>
>> Charles Greathouse
>> Analyst/Programmer
>> Case Western Reserve University
>>
>>
>> On Thu, Mar 6, 2014 at 7:57 PM, David Wilson 
<davidwwilson at comcast.net
>> >wrote:
>>
>> > Largest zeroless p-smooth number for the first few primes p.
>> >
>> >
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