A340700 Lower of a pair of adjacent perfect powers, both with exponents > 2.
27, 64, 125, 243, 1000, 1296, 2187, 50625, 59049, 194481, 279841, 456533, 614125, 3111696, 6434856, 22665187, 25411681, 38950081, 62742241, 96059601, 131079601, 418161601, 506250000, 741200625, 796594176, 1249198336, 2136719872, 2217342464, 5554571841, 5802782976
Offset: 1
Keywords
Examples
Initial terms of sequences A340700 .. A340706: a(n) = x^p, A340701(n) = A340703(n)^A340705(n) = y^q, A340706(n) = A340701(n) - a(n) = y^q - x^p. . n a(n) x ^ p A340701 y ^ q A340706 adjacent squares 1 27 = 3 ^ 3, 32 = 2 ^ 5, 5 5^2=25, 6^2=36 2 64 = 2 ^ 6, 81 = 3 ^ 4, 17 8^2=64, 9^2=81 3 125 = 5 ^ 3, 128 = 2 ^ 7, 3 11^2=121, 12^2=144 4 243 = 3 ^ 5, 256 = 2 ^ 8, 13 15^2=225, 16^2=256 5 1000 = 10 ^ 3, 1024 = 2 ^ 10, 24 31^2=961, 32^2=1024 6 1296 = 6 ^ 4, 1331 = 11 ^ 3, 35 36^2=1296, 37^2=1369 7 2187 = 3 ^ 7, 2197 = 13 ^ 3, 10 46^2=2116, 47^2=2209 8 50625 = 15 ^ 4, 50653 = 37 ^ 3, 28 225^2=50625, 226^2=51076 9 59049 = 3 ^ 10, 59319 = 39 ^ 3, 270 243^2=59049, 244^2=59536
Links
- Hugo Pfoertner, Table of n, a(n) for n = 1..1670
- StackExchange MathOverflow, Are there ever three perfect powers between consecutive squares? Answers by Gjergji Zaimi and Felipe Voloch (2011).
- Michel Waldschmidt, Perfect Powers: Pillai's works and their developments, arXiv:0908.4031 [math.NT], 27 Aug 2009.
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