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+ The largest known prime factor in "The Octopus" (as of February 3, 2010). It occurs as a(16) in the 7R arm:

2R
                                                         2=a(1)
                                                        22=a(2)
                                                       222=a(3)
                                                      6222=a(4)
                                                     96222=a(5)
                                                   9396222=a(6)
                                                6279396222=a(7)
                                            12546279396222=a(8)
                                        148212546279396222=a(9)
                                     300148212546279396222=a(10)
                                18333300148212546279396222=a(11)
                           3795318333300148212546279396222=a(12)
                     1520433795318333300148212546279396222=a(13)
               5055121520433795318333300148212546279396222=a(14)
        49840565055121520433795318333300148212546279396222=a(15)
2623287849840565055121520433795318333300148212546279396222=a(16)
                                                         ?=a(17)
Let a(1)=2. a(n) is the smallest number > a(n-1) containing a(n-1) as rightmost digits and having exactly n distinct prime factors.

Can you find the next term?
Honaker: a(1)-a(4)
Gupta: a(5)-a(14)
Andersen: a(15)-a(16)
2L
 a(1)=2 
 a(2)=21
 a(3)=2109 
 a(4)=21098 
 a(5)=2109822 
 a(6)=2109822078
 a(7)=2109822078054
 a(8)=2109822078054306 
 a(9)=2109822078054306590
a(10)=21098220780543065904030
a(11)=2109822078054306590403010890
a(12)=210982207805430659040301089001530
a(13)=21098220780543065904030108900153044430
a(14)=? 
Let a(1)=2. a(n) is the smallest number > a(n-1) containing a(n-1) as leftmost digits and having exactly n distinct prime factors.

Can you find the next term?
Honaker: a(1)-a(4)
Gupta: a(5)-a(13)
3R
                                                                3=a(1)
                                                               33=a(2) 
                                                             1533=a(3)
                                                           491533=a(4)
                                                        112491533=a(5)
                                                     319112491533=a(6)
                                                  393319112491533=a(7)
                                               964393319112491533=a(8)
                                          15905964393319112491533=a(9)
                                      598515905964393319112491533=a(10)
                                 16359598515905964393319112491533=a(11)
                            2217916359598515905964393319112491533=a(12)
                      3026852217916359598515905964393319112491533=a(13)
               11875083026852217916359598515905964393319112491533=a(14)
        340161911875083026852217916359598515905964393319112491533=a(15)
73778782340161911875083026852217916359598515905964393319112491533=a(16)
                                                                ?=a(17)
Let a(1)=3. a(n) is the smallest number > a(n-1) containing a(n-1) as rightmost digits and having exactly n distinct prime factors.

Can you find the next term?
Honaker: a(1)-a(4)
Gupta: a(5)-a(13)
Andersen: a(14)-a(16)
3L
 a(1)=3
 a(2)=33
 a(3)=3302
 a(4)=33022
 a(5)=3302222
 a(6)=330222230
 a(7)=330222230030
 a(8)=330222230030055
 a(9)=330222230030055935
a(10)=3302222300300559358065
a(11)=330222230030055935806507470
a(12)=33022223003005593580650747061518
a(13)=33022223003005593580650747061518135430
a(14)=? 
Let a(1)=3. a(n) is the smallest number > a(n-1) containing a(n-1) as leftmost digits and having exactly n distinct prime factors.

Can you find the next term?
Honaker: a(1)-a(4)
Gupta: a(5)-a(13)
5R
                                                        5=a(1)
                                                       15=a(2)
                                                      615=a(3)
                                                    18615=a(4)
                                                  5718615=a(5)
                                               1055718615=a(6)
                                            1291055718615=a(7)
                                          911291055718615=a(8)
                                      3333911291055718615=a(9)
                                   2183333911291055718615=a(10)
                              177872183333911291055718615=a(11)
                         51415177872183333911291055718615=a(12)
                    1293551415177872183333911291055718615=a(13)
              2250601293551415177872183333911291055718615=a(14)
       74586822250601293551415177872183333911291055718615=a(15)
574883974586822250601293551415177872183333911291055718615=a(16)
                                                        ?=a(17)
Let a(1)=5. a(n) is the smallest number > a(n-1) containing a(n-1) as rightmost digits and having exactly n distinct prime factors.

Can you find the next term?
Honaker: a(1)-a(4)
Gupta: a(5)-a(14)
Andersen: a(15), a(16)
5L
 a(1)=5
 a(2)=51
 a(3)=518
 a(4)=5187
 a(5)=518738 
 a(6)=518738066 
 a(7)=518738066022 
 a(8)=518738066022891 
 a(9)=5187380660228910138
a(10)=51873806602289101381770
a(11)=5187380660228910138177036634 
a(12)=51873806602289101381770366340485
a(13)=51873806602289101381770366340485096495
a(14)=? 
Let a(1)=5. a(n) is the smallest number > a(n-1) containing a(n-1) as leftmost digits and having exactly n distinct prime factors.

Can you find the next term?
Honaker: a(1)-a(4)
Gupta: a(5)-a(13)
7R
                                                                7=a(1)
                                                               57=a(2) 
                                                              357=a(3)
                                                            51357=a(4)
                                                          3451357=a(5)
                                                       1193451357=a(6)
                                                    6391193451357=a(7)
                                                20466391193451357=a(8)
                                            699320466391193451357=a(9)
                                       20508699320466391193451357=a(10)
                                  3802320508699320466391193451357=a(11)
                            5990603802320508699320466391193451357=a(12)
                      7950455990603802320508699320466391193451357=a(13)
                8621077950455990603802320508699320466391193451357=a(14)
        108013858621077950455990603802320508699320466391193451357=a(15)
11428690108013858621077950455990603802320508699320466391193451357=a(16)
                                                                ?=a(17)
Let a(1)=7. a(n) is the smallest number > a(n-1) containing a(n-1) as rightmost digits and having exactly n distinct prime factors.

Can you find the next term?
Honaker: a(1)-a(4)
Gupta: a(5)-a(13)
Andersen: a(14)-a(16)
7L
 a(1)=7 
 a(2)=74
 a(3)=741
 a(4)=74102
 a(5)=7410255
 a(6)=741025545
 a(7)=741025545195
 a(8)=741025545195705 
 a(9)=7410255451957051086
a(10)=741025545195705108602109
a(11)=7410255451957051086021092590 
a(12)=741025545195705108602109259078965
a(13)=74102554519570510860210925907896578105
a(14)=? 
Let a(1)=7. a(n) is the smallest number > a(n-1) containing a(n-1) as leftmost digits and having exactly n distinct prime factors.

Can you find the next term?
Honaker: a(1)-a(4)
Gupta: a(5)-a(13)




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