Convert it! (Problem 7)

Number Theory Level 2

What is the next term (in base 10) in the sequence below?

1 5 , 2 3 4 , 1010 1 2 , 158 5 9 , 64215 5 7 , ? 10 1_5, 23_4, 10101_2, 1585_9, 642155_7, ?_{10}


The answer is 312211.

B D by B D , 16, Bulgaria

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1 solution

Chew-Seong Cheong
Mar 23, 2020

1 5 = 1 10 Read: one 1 2 3 4 = 11 10 Read: two 1 1010 1 2 = 2 1 10 Read: one 2 one 1 158 5 9 = 121 1 10 Read: one 1 one 2 two 1 64215 5 7 = 11122 1 10 Read: three 1 two 2 one 1 ? 10 = 312211 10 \begin{array} {rl} 1_5 = 1_{10} & \small \red{\text{Read: one 1}} \\ 23_4 = \red{11}_{10} & \small \text{Read: two 1} \\ 10101_2 = 21_{10} & \small \text{Read: one 2 one 1} \\ 1585_9 = 1211_{10} & \small \text{Read: one 1 one 2 two 1} \\ 642155_7 = 111221_{10} & \small \text{Read: three 1 two 2 one 1} \\ ?_{10} = \boxed{312211}_{10} \end{array}

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Great solution!

B D - 1 year, 2 months ago

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