# [seqfan] Re: A175347: Primes in A176303

Charles Greathouse charles.greathouse at case.edu
Sun Apr 18 21:51:15 CEST 2010

```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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>>
>
>
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```