Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

2022 AMC 10B Problems/Problem 6

Revision as of 16:10, 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 \...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

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

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2022_AMC_10B_Problems/Problem_6&oldid=181888"