Pillai's Theorem

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 u_n be the nth term in the sequence. Then u_(n+1)-u_n tends to infinity nearly as rapidly as u_n.

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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."

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Pillai's Theorem

Cite this as:

Weisstein, Eric W. "Pillai's Theorem." From MathWorld--A Wolfram Web Resource.

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