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 A045575 Nonnegative numbers of the form x^y - y^x, for x,y > 1. 3
 0, 1, 7, 17, 28, 79, 118, 192, 399, 431, 513, 924, 1844, 1927, 2800, 3952, 6049, 7849, 8023, 13983, 16188, 18954, 32543, 58049, 61318, 61440, 65280, 130783, 162287, 175816, 255583, 261820, 357857, 523927, 529713, 1038576, 1048176 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Pillai proved that there are ~ 0.5 * (log x)^2/(log log x)^2 members of this sequence up to x. - Charles R Greathouse IV, Jul 20 2017 REFERENCES S. S. Pillai, On the indeterminate equation x^y - y^x = a, Journal Annamalai University 1, Nr. 1, (1932), pp. 59-61. Cited in Waldschmidt 2009. LINKS Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe) Michel Waldschmidt, Perfect Powers: Pillai's works and their developments, arXiv:0908.4031 [math.NT], 2009. MAPLE N:= 10^8: # to get all terms <= N A:= (0, 1): for x from 2 while x^(x+1) - (x+1)^x <= N do    for y from x+1 do       z:= x^y - y^x;       if z > N then break       elif z > 0 then A:=A, z;       fi od od: {A}; # Robert Israel, Aug 20 2014 MATHEMATICA Union[Flatten[Table[If[a^b-b^a>-1&&a^b-b^a<10^6*2, a^b-b^a], {a, 1, 123}, {b, a, 144}]]] (* Vladimir Joseph Stephan Orlovsky, Apr 26 2008 *) nn=10^50; n=1; Union[Reap[While[n++; k=n+1; num=Abs[n^k-k^n]; num

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Last modified April 10 02:39 EDT 2020. Contains 333392 sequences. (Running on oeis4.)