[seqfan] Re: More composite numbers are needed for A226181

[Max Alekseyev]

A couple more terms:

12816*2^13 + 1 = 104988673,
16384*2^8178 + 1

On Mon, May 26, 2014 at 9:59 AM, Max Alekseyev <maxale at gmail.com> wrote:
> Some more composite terms n (may be not in order):
>
> 64*2^26 + 1 = 4294967297,
> 128*2^57 + 1 = 18446744073709551617,
> 256*2^120 + 1 = 340282366920938463463374607431768211457,
> 512*2^247 + 1,
> 1024*2^502 + 1,
> 2048*2^1013 + 1,
> 4096*2^2036 + 1,
> 8192*2^4083 + 1
>
> Here the first factor in each expression for n is the multiplicative
> order of 2 modulo n (in other words, the period on 1/n in binary).
> Quite interesting, here they all are powers of 2 -- this does not hold
> for smaller terms however -- e.g., 12801 = 200*2^6 + 1.
>
> Regards,
> Max
>
>
> On Sun, May 25, 2014 at 9:04 AM, Tw Mike <mt.kongtong at gmail.com> wrote:
>> Dear seqfans,
>>
>> OEIS A226181:
>>
>> 3, 5, 7, 11, 13, 17, 19, 23, 29, 37, 41, 47, 53, 59, 61, 67, 71, 73, 79,
>> ...
>> Primes p such that p−1 divided by the period of the binary expansion of 1/p
>> equals 2^x for some nonnegative integer x.
>>
>> Composite numbers matching the conditions below 108 are:
>> 12801, 348161, 3225601
>>
>> Maybe all composite numbers matching the conditions are both Poulet numbers
>> and Proth numbers, but Joni Teräväinen say suspect that there is an n such
>> that n satisfies the condition but is not a Proth number. So more composite
>> numbers for A226181 are needed.
>>
>> See the related question at mathoverflow: Are all counterexamples of OEIS
>> A226181 both Poulet numbers and Proth numbers? taged by nt.number-theory,
>> prime-numbers and sequences-and-series
>>
>> Yours mike,
>>
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