[seqfan] Re: OEIS sequences needing factors

[Sean A. Irvine]

I'm the author of this list, readers should feel free to email me directly
(sairvin at xtra.co.nz or sairvin at gmail.com) with new results or suggestions
for additions to this list.  That way we can avoid cluttering up seqfan
mailing list with lots of little updates.

I can post a summary of progress or new additions every couple of months.
Alternatively, perhaps it could just be added into the OEIS wiki somewhere.

Sean.

On 03/21/13 13:31, Charles Greathouse wrote:
> Mersenneforum.org is a discussion board for those interested in
> factorization and primality searches. I've seen the above-titled thread pop
> up a few times and I thought I would advertise it here. It comes with the
> comment:
>
> **
> Please check with corresponding OEIS entry and with factordb.com to make
> sure number still needed before embarking on a significant effort.
> **
>
> Here's the list they have now. If you have suggestions for other sequences
> needing nontrivial factors, feel free to post there or reply here.
>
> id      size          description                       known ecm effort
> --------------------------------------------------------------------------------
> A000945 C335          EuclidMullin52                    7557 at 43e6
> A000946 C332          A000946(15)                       1000 at 1m,192 at 85e7
> A005265 C367                                            4590 at 11e6
> A005266 C211                                            7771 at 43e6
> A037274 C210          HP49(117)                         132 at 85e7 [likely
> more]
> A048986 C142          HP[2]2295                         4590 at 11e6
> A046461 C1252       * Sm(1051)                          1000 at 1e6
> A051308 C347          EuclidMullin[5]58                 7771 at 43e6
> A051309 C315          EuclidMullin[11]56                7771 at 43e6
> A051334 C328          EuclidMullin[8191]60              4590 at 11e6
> A051335 C564          EuclidMullin[127]66               1000 at 1e6
> A056756 C335        * EuclidMullin52                    7557 at 43e6
> A063684 C187        * 114!+1                            17900 at 11e7
> ,20084 at 85e7
> A072288 Cbig        * 10^(10^100)+2, need factor > 16
> A076670 Cbig        * (10^9)^(10^9)+1
> A078778 C187        * 114!+1                            17900 at 11e7
> ,20084 at 85e7
> A078781 C265        * 151!-1                            17900 at 11e7
> A078814 Cbig        * 10^(10^100)-7, need factor > 16
> A080802 C265          151!-1                            17900 at 11e7
> A080892 C241        * 3^505-2                           4590 at 11e6
> A081715 C246        * 3^514+2                           4590 at 11e6
> A082869 C286        * 3^599-2^599                       4590 at 11e6
> A085745 C373        * 2^1239+1239                       7771 at 43e6
> A085747 C158          100!+179                          4590 at 11e6
> A087021 C242,C271   * 10^646-1
> A096225 C106520655  * 15750503!+1
> A093782 C429        * EuclidMullin[8581]31              4590 at 11e6
> A094152 C398          EuclidMullin[32687]51             1000 at 1e6
> A095194 C163          10*102!+1                         4600 at 11e6
> A098594 C1038       * 464!+1 or C1038 464!-1            1000 at 1e6,10 at 11e6 on
> both[NEW PROGRESS]
> A099954 C377        * F(1801) [F^R(1801) is semiprime]  15000 at 11e7
> A100013 C154          105!+7                            4590 at 1e6
> A101757 C288        * Tribonacci(1091)                  4590 at 11e6
> A102050 C16385      * 10^(2^14)+1                       200 at 1e6
> A109757 C414        * tens_complement_factorial(191)+1
> A109758 C183        * tens_complement_factorial(112)-1  4590 at 11e6
> A113773 C285        *                                   4590 at 11e6
> A113913 C318        * 3^(3^7)+1                         1000 at 1e6,200 at 11e6
> A115101 C387        * L(2602)                           7771 at 43e6
> A115973 C214        * 137^137+1                         1000 at 1e6
> A122119 C716        * 2^(2^10)+5^(2^10)                 100 at 10000
> A125037 C2117                                           1000 at 1e6
> A125038 C1164       *                                   1000 at 1e6
> A125039 C160        *                                   4590 at 11e6
> A125040 C593        *                                   1000 at 1e6
> A125041 C160        *                                   4590 at 11e6
> A125042 C193        *                                   4590 at 11e6
> A125043 C1766       *                                   1000 at 1e6
> A125044 C2995                                           1000 at 1e6[need to
> confirm smallest before moving on]
> A125045 C347        *                                   4590 at 11e6
> A130139 C364        *                                   4590 at 11e6
> A130140 C36562      *                                   100 at 10000
> A130141 C235        *                                   4590 at 11e6
> A153357 C148        * Wol(347)                          4590 at 11e6
> A165767 C202        * 2^669-669                         7771 at 43e6
> A177892 C241        *                                   4590 at 11e6
> A181186 C162          (2^101-1)*101!+1                  1000 at 1e6
> A181764 C187        * 114!+1                            17900 at 11e7
> ,20084 at 85e7
> A185121 C16385      * 10^(2^14)+1                       200 at 1e6
> A195264 C156        * Alonso20(102)                     4600 at 11e6
> A199295 C15151336   * 8^(8^8)+1
> A200918 C479894     * (3^1006003-3)/1006003^2           2 at 1000,1 at 2000,1 at 5000
> ,1 at 10000
>
> http://mersenneforum.org/showthread.php?t=14265&page=3
>
> Charles Greathouse
> Analyst/Programmer
> Case Western Reserve University
>
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