Let ⌈x⌉ denote the smallest integer greater than or equal to x. The sequence (a_i) is defined as follows: a₁=1, and for all i≥1,

a_i+1=min(7⌈(a_i+1)/7⌉, 19⌈(a_i+1)/19⌉)

Compute a₁₀₀.