MathDB

The sequence

(a_n)

satisfies a_1 \equal{} 1 and \displaystyle 5^{(a_{n\plus{}1}\minus{}a_n)} \minus{} 1 \equal{} \frac{1}{n\plus{}\frac{2}{3}} for

n \geq 1

. Let

k

be the least integer greater than

1

for which

a_k

is an integer. Find

k

Problem Statement