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%I #5 Jun 12 2016 02:35:18
%S 1,3,1,8,2,9,15,37,17,25,4,19,44,20,9,40,54,19,18,57,71,28,17,64,104,
%T 53,217,55,112,100,39,24,89,156,106,35,38,113,190,128,47,36,121,208,
%U 172,81,12,107,204,244,143,40,65,172,281,239,126,11,106,225,346
%N Absolute difference between A000290(n) and the nearest term of A000578.
%C Marshall Hall, Jr. conjectured that there exists a constant c > 0 such that for any integers x and y with y^2 != x^3 the relation abs(y^2 - x^3) > c*sqrt(abs(x)) holds.
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Hall%27s_conjecture">Hall's conjecture</a>.
%o (PARI) nearestcube(n) = my(x=n-1, y=n+1); while(!ispower(x, 3) && !ispower(y, 3), x--; y++); if(ispower(x, 3), return(x)); if(ispower(y, 3), return(y))
%o a(n) = abs(n^2 - nearestcube(n^2))
%Y Cf. A078933, A199496, A199497, A199498.
%K nonn
%O 1,2
%A _Felix Fröhlich_, Jun 04 2016