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A273927
Absolute difference between A000290(n) and the nearest term of A000578.
0
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, 53, 217, 55, 112, 100, 39, 24, 89, 156, 106, 35, 38, 113, 190, 128, 47, 36, 121, 208, 172, 81, 12, 107, 204, 244, 143, 40, 65, 172, 281, 239, 126, 11, 106, 225, 346
OFFSET
1,2
COMMENTS
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.
PROG
(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))
a(n) = abs(n^2 - nearestcube(n^2))
CROSSREFS
KEYWORD
nonn
AUTHOR
Felix Fröhlich, Jun 04 2016
STATUS
approved