[seqfan] Re: A175347: Primes in A176303
Charles Greathouse
charles.greathouse at case.edu
Mon Apr 19 14:15:25 CEST 2010
11647 and 19223 are also in the sequence of exponents; no more terms
through 78815.
Charles Greathouse
Analyst/Programmer
Case Western Reserve University
On Sun, Apr 18, 2010 at 3:51 PM, Charles Greathouse
<charles.greathouse at case.edu> wrote:
> I also think the original sequence should be rifo (retired in favor
> of) the sequence of exponents.
>
> There are many more congruence relations, if you're interested:
> The exponents must be 7 mod 8: 17 | 2^(8n + 3) - 127.
> The exponents cannot be 0 mod 3: 7 | 2^(3n) - 127.
>
> Just using these two, Pari code looks like
> forstep(n=7,1e4,[16,8],k=2^n-127;if(ispseudoprime(k),print1(n",")))
>
> Other bad residue classes: Mod(9, 10), Mod(5, 18), Mod(10, 11),
> Mod(31, 52), Mod(11, 28), Mod(30, 83). If you're going to test very
> high, it's probably worthwhile to search for forms like this. (It's
> easy to produce a list of thousands.)
>
> Charles Greathouse
> Analyst/Programmer
> Case Western Reserve University
>
> On Sun, Apr 18, 2010 at 2:20 PM, Maximilian Hasler
> <maximilian.hasler at gmail.com> wrote:
>> Oh no, thanks, but you deserve the credits for you since it was your idea.
>> The computation of the additional terms takes less than a minute,
>> with completely trivial PARI code, so it's no significant contribution.
>> And I don't have the time do work out a more substantial contribution.
>> A rather trivial observation is:
>>
>> All terms (indices) must be of the form n=4k+3, because
>> * if n is even, then 2^n-127 = 0 (mod 3)
>> * If n=4k+1, then 2^n-127 = 0 (mod 5)
>>
>> Regards,
>> Maximilian
>>
>> PS: I checked that there are no more terms up to 10^4.
>>
>>
>> On Sun, Apr 18, 2010 at 7:43 PM, zak seidov <zakseidov at yahoo.com> wrote:
>>> Sure,
>>> it'd be better.
>>> You may wish to submit it
>>> (and remove A175347).
>>> Zak
>>>
>>>
>>>> From: Maximilian Hasler <maximilian.hasler at gmail.com>
>>>> Subject: [seqfan] Re: A175347: Primes in A176303
>>>> To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
>>>> Date: Sunday, April 18, 2010, 1:35 PM
>>>> Maybe it would be more "economical"
>>>> to list the exponents (indices of
>>>> A176303) rather than the primes themselves...
>>>> That sequence would go on:
>>>>
>>>> 47,55,103,143, 391, 2807,
>>>>
>>>> the next term is > 8000.
>>>>
>>>> Maximilian
>>>>
>>>> On Sun, Apr 18, 2010 at 6:31 PM, zak seidov <zakseidov at yahoo.com>
>>>> wrote:
>>>> > Just submitted.
>>>> > Zak
>>>> >
>>>> >> Subject: NEW SEQUENCE FROM submitN Zak Seidov
>>>> A175347
>>>> >
>>>> >> Date: Sunday, April 18, 2010, 12:40 PM
>>>> >
>>>> >> %S A175347
>>>> >>
>>>> 140737488355201,36028797018963841,10141204801825835211973625642881,
>>>> >> %T A175347
>>>> 11150372599265311570767859136324180752990081
>>>> >> %N A175347 Primes in A176303.
>>>> >> %C A175347 These are 2^n-127 for n =
>>>> {47,55,103,143}.
>>>
>>>>
>>>
>>>
>>>
>>>
>>>
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>>>
>>
>>
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