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M&M (Posted on 2004-11-26) Difficulty: 3 of 5

What comes next in the following sequence?

1212210202001, 224000000, 11333311, 623351, 290221, ...?

See The Solution Submitted by Erik O.    
Rating: 2.0000 (2 votes)

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Solution solution | Comment 1 of 4

The representation of one million in odd bases, starting with 3 are:

3            1212210202001
5            224000000
7            11333311
9            1783661
11           623351
13           290221
15           14B46A
17           BG939
19           7CF1B
21           52KC1
23           3D486
25           2E000
27           1NLK1
29           1C01M
31           12HI2
33           RR91
35           NBBF
37           JRH1
39           GXI1
41           EKA
43           COZZ (that's a letter O)

where A, B, C, etc. are used to represent values of 10, 11, 12, etc., so the next one in sequence is 14B46A.

Alternatively you might want to represent this as 14(11)46(10), as in the following table:

15           14(11)46(10)
17           (11)(16)939
19           7(12)(15)1(11)
21           52(20)(12)1
23           3(13)486
25           2(14)000
27           1(23)(21)(20)1
29           1(12)01(22)
31           12(17)(18)2
33           (27)(27)91
35           (23)(11)(11)(15)
37           (19)(27)(17)1
39           (16)(33)(18)1
41           (14)(20)(36)(10)
43           (12)(24)(35)(35)
45           (10)(43)(37)(10)
47           9(29)(32)(28)
49           8(24)(24)8
51           7(27)(23)(43)
53           6(37)(52)(49)
55           60(31)(45)
57           5(22)(44)(49)
59           4(51)(16)9
61           4(24)(45)(27)
63           3(62)(60)1
65           3(41)(44)(40)
67           3(21)(51)(25)
69           332(52)
71           2(56)(26)(36)
73           2(41)(47)(46)
75           2(27)(58)(25)
77           2(14)(51)1
79           22(18)(18)
81           1(71)(33)(55)
83           1(62)(13)(16)
85           1(53)(34)(60)
87           1(45)(10)(22)
89           1(37)(21)(85)
91           1(29)(69)1
93           1(22)(57)(64)
95           1(15)(76)(30)
97           19(27)(27)
99           1331

  Posted by Charlie on 2004-11-26 20:08:07
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