Data Chip cost formula
On Hard Mode, the n-th Data Chip costs $1,000,000 * 2^(n-1). Chips 1-6 cost $1M, $2M, $4M, $8M, $16M, and $32M for a cumulative $63M without Super Researcher.
Why Super Researcher is optimal
Super Researcher grants one free starting chip, which removes the $32M sixth-chip tier. The total drops from $63M to $31M, a $32M (50.79%) savings. It is the highest-leverage first rebirth perk in the game.
Perk order for Hard Mode
Buy Super Researcher first, Farm and Mine Boost second, and Ice and Water Upgrader third. Save the third token until you have the three trophies and the Collector badge.