A253181 Numbers n such that the distance between n^3 and the nearest square is less than n.

1, 2, 3, 4, 5, 9, 13, 15, 16, 17, 25, 32, 35, 36, 37, 40, 43, 46, 49, 52, 56, 63, 64, 65, 81, 99, 100, 101, 109, 121, 136, 143, 144, 145, 152, 158, 169, 175, 190, 195, 196, 197, 225, 243, 255, 256, 257, 289, 312, 317, 323, 324, 325, 331, 336, 351, 356, 361, 366, 377

Offset: 1

Author

Alex Ratushnyak, Mar 23 2015

Keywords

• nonn

Comments

Distance can be zero, that is, cubes that are squares are included.

Numbers n such that A002938(n) < n.

Examples

			The distance between 5^3=125 and the nearest square 11^2=121 is less than 5, so 5 is in the sequence.
		

Links

• Daniel Mondot, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000290, A000578, A002760.

Cf. A116885, A002938, A077119.

Cf. A268509, A268510.

Programs

Mathematica

dnsQ[n_]:=Module[{n3=n^3,sr},sr=Sqrt[n3];Min[n3-Floor[sr]^2, Ceiling[ sr]^2- n3]Harvey P. Dale, Dec 23 2015 *)

Python

def isqrt(a):
    sr = 1 << (int.bit_length(int(a)) >> 1)
    while a < sr*sr:  sr>>=1
    b = sr>>1
    while b:
        s = sr + b
        if a >= s*s:  sr = s
        b>>=1
    return sr
for n in range(1000):
    cube = n*n*n
    r = isqrt(cube)
    sqr = r**2
    if cube-sqr < n or sqr+2*r+1-cube < n:  print(str(n), end=',')