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OEIS sequences needing factors

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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 to make sure number still needed before embarking on a significant effort.

id      size          description                       known ecm effort
A000945 C335          EuclidMullin52                    7557@43e6
A000946 C332          A000946(15)                       1000@85e7
A001578 C238          Fibonacci(1301)
A002582 C214          136!-1                            17900@11e7
A002583,A078778,A181764 C242     140!+1                 17900@11e7
A002584 C187          479#-1
A002585 C169          457#+1                            4590@11e6
A002587 C244          2^1009+1                            
A002588 C337          2^1207-1 or Phi{1207}(2)                     same factorization is needed by A049093, A049094, A237043 
A002590 C241          2^1028+1 or Phi_{2056}(2) 
A002591 C277          3^617-1 or Phi_{617}(3) 
A002592 C220          3^632+1 or Phi_{1264}(2) 
A003020,A081318,A102347 C271  10^323-1 or Phi_{323}(10) 
A003021 C267          10^298+1 or Phi_{596}(10) 
A005265 C367          prod(A005265(k),k=1..68)-1        4590@11e6
A005266 C211          prod(A005266(k),k=1..14)-1        17900@11e7
A006486 C234          127^127-1
A006514 C297          2^1213-1
A007571 C214          124^124+1
A016047 C385          2^1277-1 or Phi_{1277}(2)         112000@26e7 [likely more] (same factorization is needed by A085724)
A037274 C251          HP49(119)                         2*t60
A046413 C509          10^509-1 or Phi_{509}(10) 
A046461 C5497       * Sm(1651)                          4590@11e6
A046932 C332          2^1117-1 or Phi_{1117}(2) 
A048986 C189          HP[2]2295                         now at index 281
A050922 C1133         2^(2^12)+1 or or Phi_{8192}(2) 
A051308 C347          EuclidMullin[5]58                 7771@43e6
A051309 C315          EuclidMullin[11]56                7771@43e6
A051328 C743          EuclidMullin[89]79                4590@11e6
A051334 C328          EuclidMullin[8191]60              4590@11e6
A051335 C564          EuclidMullin[127]66               4590@11e6
A056756 C335        * EuclidMullin52                    7557@43e6
A057204 C1341         4*prod(A057204(k),k=1..47)^2+3    1000@1e6
A057205 C345          4*prod(A057205(k),k=1..24)-1      4590@11e6
A057206 C259        * 6*prod(A057206(k),k=1..17)-1      17900@11e7
A057207 C572          4*prod(A057207(k),k=1..41)^2+1    t45         cf.
A057208 C414          prod(A057208(k),k=1..18)^2+4      1800@11e6
A063684 C182        * 118!+2                            17900@11e7
A072288 Cbig        * 10^(10^100)+2, need factor > 16
A072381 C323          Fibonacci(1543)
A073639 C984        * 2^4495-1 or Phi_{4495}(2) 
A076670 Cbig          (10^9)^(10^9)+1
A078781,A080802 C265        * 151!-1                            17900@11e7
A078814 Cbig        * 10^(10^100)-7, need factor > 16
A080892 C314        * 3^658-2                           
A081715 C246        * 3^514+2                           4590@11e6
A082869 C286        * 3^599-2^599 or Phi_{599}(3, 2)                       4590@11e6
A085726 C383          Lucas(1831)
A085745 C373        * 2^1239+1239                       7771@43e6
A085747 C167          104!+227                          4590@11e6
A087552 C684          Concatenation of 1^1 0^2 1^3 0^4 ... 1^37 divided by (10^19-1)/9
A087021 C242,C271   * 10^646-1 or Phi_{323}(10) and or Phi_{646}(10) 
A087022 same as A087021
A091335 C416        * Sylvester(11)                     4590@11e6
A093179 C315653     * 2^(2^20)+1 or Phi_{2097152}(2) 
A093782 C429        * EuclidMullin[8581]31              4590@11e6
A094152 C398          EuclidMullin[32687]51             1000@1e6
A095194 C163          10*102!+1                         17900@11e7
A096098 C1570         concat(A096098(n),n=1..182)
A096225 C106520655  * 15750503!+1
A098594 C2356       * 929!+1                            4590@11e6
A099954 C377        * F(1801) [F^R(1801) is semiprime]  17900@11e7
A100013 C178          110!+7                            4590@11e6
A101757 C288        * Tribonacci(1091)                  4590@11e6
A102050,A185121 C16385      * 10^(2^14)+1 or    or Phi_{32768}(10)                    200@1e6
A102926 C472          a(112)=spf(a(1)*...*a(111) +/- 1) 2300@11e7 (on -), 2060@11e7 (on +)  ?   cf.
A109757 C414        * tens_complement_factorial(191)+1  4590@11e6
A109758 C183        * tens_complement_factorial(112)-1  4590@11e6
A113773 C285        *                                   4590@11e6
A113913 C317,C322   * 3^(3^7)+1 or Phi_{4374}(3)        4590@11e6
A115101 C387        * L(2602)                           7771@43e6
A115973 C214        * 137^137+1 or Phi_{274}(137)       4590@11e6
A120716 C1101       *                                   4590@11e6
A122119 C716        * 2^(2^10)+5^(2^10)  or Phi_{2048}(2, 5)                100@10000,440@1e6 [1 factor is known, swellman]
A122787 C354295     Phi_{3^12}(10)
A125037 C2117                                           1000@1e6
A125038 C1164       * Phi_{17}(5461881130856756498343881353355730200091930726446628652260883480575183173) 1000@1e6
A125039 C817                                            4590@11e6
A125040 C593        *                                   4590@11e6
A125041 C1056                                           1000@1e6
A125042 C193        *                                   17900@11e7
A125043 C1766       *                                   1000@1e6
A125044 C2995                                           1000@1e6,4590@11e6[need to confirm smallest before moving on]
A125045 C347        *                                   4590@11e6
A128677 C21101      (102^(103^2)+1)/(102^103+1) or Phi_{21218}(102) 
A130139 C364        *                                   4590@11e6
A130140 C36562      *                                   100@10000
A130141 C235        *                                   4590@11e6
A130142 C1478
A147554 C260        * 10^417-1 or Phi_{417}(10)          cf.
A153357 C160          Wol(371)                          4600@11e6
A165767 C449        * 2^1489-1489                       4590@11e6       (also needed by b-files in A165768,A165769)
A177892 C241        *                                   17900@11e7
A177996 C340          (156^157 + 1)/157^2 or Phi_{314}(156) 
A181186 C162          (2^101-1)*101!+1                  7590@11e6
A195264 C178        * Alonso20(110)                     17900@11e7
A199295 C15151336   * 8^(8^8)+1
A200918 C479894     * (3^1006002-1)/1006003^2 or Phi_{1006002}(3)      2@1000,1@2000,1@5000,1@10000
A217759 C289                                            890@43e6
A218467 C283                                            700@43e6
A246556 C179          Pell(599)                         
A249909 C310        * Euler(188)
A250288 C335        * 12^311-1  or Phi_{311}(12)        (Same factorization is needed by A252170)
A250291 C338        * 2^1123+1 or Phi_{2246}(2) 
A250292 C271        * Pell(709)                         
A250293 C188        * 457#+1
A250294 C209        * 503#-1
A250295 C210        * A005165(125)
A286181,A286208 C222 * 139!-1