Write the exact powers of 2 and 3 in sorted order as 1, 2, 3, 4, 8, 9, 16, 27, 32, ... (OEIS A006899), and let 
be the 
th term in the sequence. Then 
tends to infinity nearly as rapidly as 
.
Pillai's Theorem
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References
Hardy, G. H. Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work, 3rd ed. New York: Chelsea, 1999.Pillai. J. Indian Math. Soc. 19, 1-11, 1931.Sloane, N. J. A. Sequence A006899/M0588 in "The On-Line Encyclopedia of Integer Sequences."Referenced on Wolfram|Alpha
Pillai's TheoremCite this as:
Weisstein, Eric W. "Pillai's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PillaisTheorem.html