A116885 -id:A116885 - cp's OEIS frontend

A116884 Integers k such that 0 < |k^5 - m^2| <= k^(3/2) for some integer m.

1, 5, 8, 23, 27, 55, 73, 76, 377, 396, 432, 18219, 18231, 747343, 748635, 5523608, 7626590, 32866452, 82251007, 1133553044, 1778903359, 3664408636, 7208605769, 26149894782

Offset: 1

Giovanni Resta, Feb 27 2006

nonn

			|432^5 - 3878907^2| = 8217 < 432^(3/2).

Cf. A078933, A116885.

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

Original entry on oeis.org

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

Alex Ratushnyak, Mar 23 2015

nonn

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

Numbers n such that A002938(n) < n.

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

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

Cf. A000290, A000578, A002760.
Cf. A116885, A002938, A077119.
Cf. A268509, A268510.

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 *)

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=',')

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A116884 Integers k such that 0 < |k^5 - m^2| <= k^(3/2) for some integer m.

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

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