A273927 Absolute difference between A000290(n) and the nearest term of A000578.

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.

Links

Table of n, a(n) for n=1..61.

Wikipedia, Hall's conjecture.

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

Cf. A078933, A199496, A199497, A199498.

Sequence in context: A248584 A077111 A073072 * A293975 A185452 A179449

Adjacent sequences: A273924 A273925 A273926 * A273928 A273929 A273930

Keyword

nonn

Author

Felix Fröhlich, Jun 04 2016

Status

approved