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A253181
Numbers n such that the distance between n^3 and the nearest square is less than n.
3
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
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
KEYWORD
nonn
AUTHOR
Alex Ratushnyak, Mar 23 2015
STATUS
approved