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

1,2

Comments

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

Numbers n such that A002938(n) < n.

Links

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

Example

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

Mathematica

dnsQ[n_]:=Module[{n3=n^3, sr}, sr=Sqrt[n3]; Min[n3-Floor[sr]^2, Ceiling[ sr]^2- n3]<n]; Select[Range[400], dnsQ] (* Harvey P. Dale, Dec 23 2015 *)

Prog

(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=', ')

Crossrefs

Cf. A000290, A000578, A002760.

Cf. A116885, A002938, A077119.

Cf. A268509, A268510.

Sequence in context: A331364 A319720 A140298 * A107365 A026484 A120760

Adjacent sequences: A253178 A253179 A253180 * A253182 A253183 A253184

Keyword

nonn

Author

Alex Ratushnyak, Mar 23 2015

Status

approved