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2022 AMC 10B Problems/Problem 6

Revision as of 15:10, 17 November 2022 by MRENTHUSIASM (talk | contribs) (Created page with "==Problem== How many of the first ten numbers of the sequence <math>121, 11211, 1112111, \ldots</math> are prime numbers? <math>\textbf{(A) } 0 \qquad \textbf{(B) }1 \qquad \...")
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Problem

How many of the first ten numbers of the sequence $121, 11211, 1112111, \ldots$ are prime numbers?

$\textbf{(A) } 0 \qquad \textbf{(B) }1 \qquad \textbf{(C) }2 \qquad \textbf{(D) }3 \qquad \textbf{(E) }4$

Solution

The recursive formula for this sequence is \begin{align*} a_1 &= 121, \\ a_n &= 10a_{n-1} + 10^{2n} + 1 & \text{for }2\leq n\leq 10. \end{align*} ~MRENTHUSIASM

See Also

2022 AMC 10B (Problems • Answer Key • Resources)
Preceded by
Problem 5 		Followed by
Problem 7
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AMC 10 Problems and Solutions

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