Consider the sequence $(a_k)_{k\ge 1}$ of positive rational numbers defined by $a_1 = \frac{2020}{2021}$ and for $k\ge 1$, if $a_k = \frac{m}{n}$ for relatively prime positive integers $m$ and $n$, then

\a_{k+1} = \frac{m + 18}{n+19}.\Determine the sum of all positive integers $j$ such that the rational number $a_j$ can be written in the form $\frac{t}{t+1}$ for some positive integer $t$.

2021 aime i #10fjioowefioweijiowejiowefjiopfopefiiowfwefpoeffewop

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I-10

A US interstate highway that runs in an east-west radius in the southern portion of the United States in the states of California, Arizona, New Mexico, Texas, Louisiana, Mississippi, Alabama and Florida . It's west terminus is in Los Angeles, CA in the Santa Monica area at PCH, California State Hwy 1. It's easy terminus is in Jacksonville, Florida at Interstate US Highway 95. It runs over 2,000 miles across the county and is the 4th longest interstate highway in the United States. It runs through major cities such as Los Angeles, Phoenix, San Antonio, Houston, New Orleans, Jacksonville and many more populated cities. It can be called I-10, Interstate 10, US Interstate highway 10, and can be called 10 freeway in populated metro areas and cities.

( Dave ) Aye babe lets escape this fucking summertime heat in Phoenix and go hit up LA and Cali. How do we get there ?

( Lexie ) We just hop on the I-10 all the way west, we'll arrive in about 4-6 hours. No other routes

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I-10

the best Interstate in the USA that connects Cali to somewhere in the East; all that I know fa' sho is that it runs through Cali(LA), Arizona, New Mexico, Texas(San Antonio and Houston), Louisiana(Baton Rouge and New Orleans), and etc.

Some of these boys say I aint from the hood so I grin / I told them boys I lived most of my life on I-10.
-unknown

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