Numbers wanted for OEIS sequences - Page 6

lorgix · 2011-02-05, 21:50

I rechecked the Sm(n)'s in the file, up to B1=250k. I also ran 20curves with B1=500k.

Batalov's suggestion; B1=3e6 is probably good.

Pi₃₄₆=5*p345
Pi₄₀₂=p19*p384

Pi₄₁₈ have no known factors.
Pi₄₃₀ have no known factors.

sean · 2011-03-23, 20:01

Code:

Sm(691) = 1304238680165623831238651513722972177904593843651 * C1916

So Sm(691) is not a member of A046461, next candidate is Sm(1051).

sean · 2013-03-07, 19:21

Here is a revised list of OEIS sequences needing factors:

Code:

# The following table lists some OEIS entries for which computing further
# terms is blocked by finding at least one factor of an integer.  In some,
# cases a complete factorization is required, in others only the smallest
# factor, or any factor.
#
# The list is unlikely to be exhaustive nor does inclusion or exclusion
# from the list indicate any kind or importance or mathematical utility.
# As near as I can tell many of these sequences have no utility beyond
# their OEIS entry.
#
# Rows marked with "*" indicate more terms are needed for the initial
# sequence lines in the corresponding OEIS entry.  That is, the OEIS
# entry has (or should have) the "more" keyword.  As above, it is not
# an indication of the importance of the sequence.
#
# In some cases it is possible or likely that considerably more ECM
# effort has been expended than is indicated below.
#
# Please check with corresponding OEIS entry and with factordb.com to make
# sure number still needed before embarking on a signficiant effort.

id      size          description                       known ecm effort
--------------------------------------------------------------------------------
A000945 C335          EuclidMullin52                    7557@43e6
A000946 C332          A000946(15)                       1000@1m,192@85e7
A005265 C367                                            4590@11e6
A005266 C211                                            7771@43e6
A037274 C210          HP49(117)                         132@85e7 [likely more]
A048986 C142          HP[2]2295                         4590@11e6
A046461 C1252       * Sm(1051)                          1000@1e6
A051308 C347          EuclidMullin[5]58                 7771@43e6
A051309 C315          EuclidMullin[11]56                7771@43e6
A051334 C328          EuclidMullin[8191]60              4590@11e6
A051335 C564          EuclidMullin[127]66               1000@1e6
A056756 C335        * EuclidMullin52                    7557@43e6
A063684 C187        * 114!+1                            17900@11e7,20084@85e7
A072288 Cbig        * 10^(10^100)+2, need factor > 16
A076670 Cbig        * (10^9)^(10^9)+1                   
A078778 C187        * 114!+1                            17900@11e7,20084@85e7
A078781 C265        * 151!-1                            17900@11e7
A078814 Cbig        * 10^(10^100)-7, need factor > 16
A080802 C265          151!-1                            17900@11e7
A080892 C241        * 3^505-2                           4590@11e6
A081715 C246        * 3^514+2                           4590@11e6
A082869 C286        * 3^599-2^599                       4590@11e6
A085745 C373        * 2^1239+1239                       7771@43e6
A085747 C158          100!+179                          4590@11e6
A087021 C242,C271   * 10^646-1
A096225 C106520655  * 15750503!+1
A093782 C429        * EuclidMullin[8581]31              4590@11e6
A094152 C398          EuclidMullin[32687]51             1000@1e6
A095194 C163          10*102!+1                         4600@11e6
A098594 C1038       * 464!+1 or C1038 464!-1            1000@1e6,10@11e6 on both[NEW PROGRESS]
A099954 C377        * F(1801) [F^R(1801) is semiprime]  15000@11e7
A100013 C154          105!+7                            4590@1e6
A101757 C288        * Tribonacci(1091)                  4590@11e6
A102050 C16385      * 10^(2^14)+1                       200@1e6
A109757 C414        * tens_complement_factorial(191)+1
A109758 C183        * tens_complement_factorial(112)-1  4590@11e6
A113773 C285        *                                   4590@11e6
A113913 C318        * 3^(3^7)+1                         1000@1e6,200@11e6
A115101 C387        * L(2602)                           7771@43e6
A115973 C214        * 137^137+1                         1000@1e6
A122119 C716        * 2^(2^10)+5^(2^10)                 100@10000
A125037 C2117                                           1000@1e6
A125038 C1164       *                                   1000@1e6
A125039 C160        *                                   4590@11e6
A125040 C593        *                                   1000@1e6
A125041 C160        *                                   4590@11e6
A125042 C193        *                                   4590@11e6
A125043 C1766       *                                   1000@1e6
A125044 C2995                                           1000@1e6[need to confirm smallest before moving on]
A125045 C347        *                                   4590@11e6
A130139 C364        *                                   4590@11e6
A130140 C36562      *                                   100@10000
A130141 C235        *                                   4590@11e6
A153357 C148        * Wol(347)                          4590@11e6
A165767 C202        * 2^669-669                         7771@43e6
A177892 C241        *                                   4590@11e6
A181186 C162          (2^101-1)*101!+1                  1000@1e6
A181764 C187        * 114!+1                            17900@11e7,20084@85e7
A185121 C16385      * 10^(2^14)+1                       200@1e6
A195264 C156        * Alonso20(102)                     4600@11e6
A199295 C15151336   * 8^(8^8)+1
A200918 C479894     * (3^1006003-3)/1006003^2           2@1000,1@2000,1@5000,1@10000

Mr. P-1 · 2013-03-20, 23:10

Please add A102926 to your list. Requires the smallest factor of either of two numbers, combined with proof or reasonably certainty that the other has none smaller. I've calculated the composites as two C472s, but I haven't checked my calculation.

Mr. P-1 · 2013-03-21, 02:17

And of course, A057207(42) where a C572 needs a smallest factor.

swellman · 2013-03-21, 06:12

A125045(33) is correct. The C109 cofactor splits as follows

prp40 = 1076567886777084649043466415734174324961

prp70 = 4659260420390412050502384623942071332680543457304768396309048770543833

m_f_h · 2013-03-21, 06:16

Following posts by Charles and Sean on the SeqFan list, I've created https://oeis.org/wiki/OEIS_sequences_needing_factors
I hope it might be useful to maintain Sean's list. (Maybe it could / should be augmented with links to appropriate places where the progress is published.)
Feel free to do with that page whatever you consider useful.

m_f_h · 2013-03-21, 06:59

Quote:

Originally Posted by Mr. P-1

Please add A102926 to your list. Requires the smallest factor of either of two numbers, combined with proof or reasonably certainty that the other has none smaller. I've calculated the composites as two C472s, but I haven't checked my calculation.

I confirm the length, the two C472's are the product of earlier terms, +/- 1 (not sure whether this is a particular challenge and/or interesting for any reason beyond calculating some more terms)

A102926 = [2, 3, 5, 29, 11, 7, 13, 37, 17, 79, 23, 4129, 193, 2593, 101, 19, 39163, 577, 26431, 131, 308798542881428667318174028327605372989, 103, 163, 179, 293, 127, 6287, 683437, 31, 89, 13590243019242466336587034391, 113, 2207, 59, 109, 223, 2351, 62861, 4651, 43, 53, 669301, 1087, 7477, 817246446020375245871694881, 41, 323717, 187273, 83, 337, 1327, 431, 739, 15137, 5659, 47, 4086059, 97, 93557, 827923, 569, 281, 2129, 1033, 433, 82373, 239, 263, 1217, 719, 4931, 383, 769, 60149, 4049, 620663, 280768815947, 2229371, 73, 571, 43350011, 309059, 199, 1162597, 61, 1187, 619, 401, 11887, 39383, 69817639, 29569, 17747, 21017, 6143, 140171, 389, 4957, 167, 859, 1231, 503, 405683, 233, 4362223, 1151, 562057541839, 160970257871, 900139, 541, 542511121]
#Str(C=prod(i=1,#%,%[i]))
% = 472
apply(isprime,[C-1,C+1])
% = [0, 0]

m_f_h · 2013-03-21, 07:08

Quote:

Originally Posted by Mr. P-1

And of course, A057207(42) where a C572 needs a smallest factor.

Here I don't understand: Why a(42)? Only 16 terms are listed on OEIS. The next is is the least prime factor = 1 mod 4 of 1+4*product(a(1..16))^2. Do you have a(17)..a(41)?

LaurV · 2013-03-21, 07:41

That C141 is factored. Other terms follow for a while, I did not look up to the index 42, however.

edit: you may see here too.

Mr. P-1 · 2013-03-21, 08:18

Quote:

Originally Posted by m_f_h

Here I don't understand: Why a(42)? Only 16 terms are listed on OEIS. The next is is the least prime factor = 1 mod 4 of 1+4*product(a(1..16))^2. Do you have a(17)..a(41)?

Quote:

Originally Posted by Mr. P-1

And of course, A057207(42) where a C572 needs a smallest factor.

Click on the C572!!!

2011-03-23, 20:01	#57
sean Aug 2004 New Zealand 223 Posts	Code: Sm(691) = 1304238680165623831238651513722972177904593843651 * C1916 So Sm(691) is not a member of A046461, next candidate is Sm(1051).

2013-03-20, 23:10	#59
Mr. P-1 Jun 2003 1169₁₀ Posts	Please add A102926 to your list. Requires the smallest factor of either of two numbers, combined with proof or reasonably certainty that the other has none smaller. I've calculated the composites as two C472s, but I haven't checked my calculation. Last fiddled with by Mr. P-1 on 2013-03-20 at 23:13

2013-03-21, 06:16	#62
m_f_h Feb 2007 2⁴·3³ Posts	Sean's list on the OEIS wiki Following posts by Charles and Sean on the SeqFan list, I've created https://oeis.org/wiki/OEIS_sequences_needing_factors I hope it might be useful to maintain Sean's list. (Maybe it could / should be augmented with links to appropriate places where the progress is published.) Feel free to do with that page whatever you consider useful.

2013-03-21, 07:41	#65
LaurV Romulan Interpreter Jun 2011 Thailand 7×1,373 Posts	That C141 is factored. Other terms follow for a while, I did not look up to the index 42, however. edit: you may see here too. Last fiddled with by LaurV on 2013-03-21 at 07:47

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2011-02-05, 21:50	#56
lorgix Sep 2010 Scandinavia 3·5·41 Posts	I rechecked the Sm(n)'s in the file, up to B1=250k. I also ran 20curves with B1=500k. Batalov's suggestion; B1=3e6 is probably good. Pi₃₄₆=5p345 Pi₄₀₂=p19p384 Pi₄₁₈ have no known factors. Pi₄₃₀ have no known factors.

2013-03-21, 02:17	#60
Mr. P-1 Jun 2003 2221₈ Posts	And of course, A057207(42) where a C572 needs a smallest factor.

2013-03-21, 06:12	#61
swellman Jun 2012 2²×13×59 Posts	A125045(33) is correct. The C109 cofactor splits as follows prp40 = 1076567886777084649043466415734174324961 prp70 = 4659260420390412050502384623942071332680543457304768396309048770543833