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Next Numbers Please #4 (Posted on 2004-11-16) Difficulty: 5 of 5
What are the next two numbers in this sequence:

1, 2, 4, 16, 26, 42, 57, 512, 730, 1010, 1343, 1872, 2367, 2954

See The Solution Submitted by Brian Smith    
Rating: 3.0000 (6 votes)

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Some Thoughts re: Hint | Comment 3 of 13 |

(In reply to Hint by Brian Smith)

"A hint: change of base is very important in this sequence."

Assuming the original series is in base 10 and we have to change it to something else:

To Base 2: 1, 10, 100, 10000, 11010, 101010, 111001, 1000000000, 1011100010, 1111110010, 10101000001, 11101010000, 100100111111, 101110001010, ?

To Base 3: 1, 2, 11, 121, 222, 1120, 2010, 200222, 1000100, 1101102, 1211211, 2120100, 1002020, 1100110, ?

To Base 4: 1, 2, 10, 100, 122, 222, 321, 20000, 23202, 33302, 111001, 131100, 210333, 232022, ?

To Base 5: 1, 2, 4, 31, 101132, 212, 4022, 10423, 13020, 20340, 24442, 33432, 43304, ?

To Base 6: 1, 2, 4, 24, 42, 110, 133, 2212, 3230, 4402, 10121, 12400, 14543, 21402, ?

To Base 7: 1, 2, 4, 22, 35, 60, 111, 1331, 2103, 2642, 3631, 5313, 6621, 11420, ?

To Base 8: 1, 2, 4, 20, 32, 52, 71, 1000, 1342, 1762, 2501, 3520, 4477, 5612, ?

To Base 9: 1, 2, 4, 17, 28, 46, 63, 628, 1010, 1342, 1754, 2510, 3220, 4042, ?

Already in Base 10: 1, 2, 4, 16, 26, 42, 512, 738, 1010, 1345, 1872, 2367, 2954, ? (see problem)

To Base 11: 1, 2, 4, 15, 24, 39, 52, 426, 611, 839, 1013, 1452, 1862, 2246, ?

To Base 12: 1, 2, 4, 14, 22, 36, 49, 368, 516, 702, 941, 1100, 1453, 1862, ?

Assuming the problem is in some other base and needs to be changed to base 10 (I start at base 11 because there are '9's in the problem):

From Base 11: 1, 2, 4, 17, 28, 46, 62, 618, 888, 1342, 1743, 2378, 3098, 3810, ?

From Base 12: 1, 2, 4, 18, 30, 50, 67, 734, 1052, 1740, 2213, 2966, 3967, 4816, ?

From Base 13: 1, 2, 4, 19, 32, 54, 72, 860, 1230, 2210, 2761, 3642, 4986, 5984, ?

From Base 14: 1, 2, 4, 20, 34, 58, 77, 996, 1422, 2758, 3393, 4412, 6167, 7326, ?

From Base 15: 1, 2, 4, 21, 36, 62, 82, 1142, 1628, 3390, 4115, 5282, 7522, 8854, ?

From Base 16: 1, 2, 4, 22, 38, 66, 87, 1298, 1848, 4112, 4933, 6258, 9063, 10580, ?

I don't see any pattern whatsoever, so I must be going at it incorrectly.  I'll keep trying.

Edited on November 18, 2004, 12:50 am

Edited on November 18, 2004, 1:02 am
  Posted by Dustin on 2004-11-18 00:48:51

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