A199497 -id:A199497 - cp's OEIS frontend

A199498 Values y for positive good examples of Hall's conjecture: positive integers d = x^3-y^2 < sqrt(x).

223063347, 911054064, 929989991784733049, 43868513629203032816, 211477180624706647625, 447884928428402042307918, 3583079427427216338463344, 7441505802879036345061579, 182720147509505842286585077, 31012309752051601656131750312, 277382747164996776244709473092

Offset: 1

Artur Jasinski, Nov 07 2011

nonn

For values x see A199496.

For values d see A199497.

Cf. A078933, A199496, A199497.

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

Original entry on oeis.org

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

Felix Fröhlich, Jun 04 2016

nonn

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.

Wikipedia, Hall's conjecture.

Cf. A078933, A199496, A199497, A199498.

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))

cp's OEIS Frontend

A199498 Values y for positive good examples of Hall's conjecture: positive integers d = x^3-y^2 < sqrt(x).

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

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