A238599 Numbers k such that k+x+y is a perfect cube, where x and y are the two cubes nearest to k.

0, 29, 171, 476, 1015, 1044, 1907, 3142, 4815, 7093, 9882, 13313, 17452, 22580, 28393, 35118, 42821, 43120, 51939, 61874, 72991, 85835, 99604, 114759, 131366, 150192, 170009, 191482, 214677, 240625, 267588, 296477, 327358, 361568, 396775, 434178, 473843, 475306, 517455

Offset: 1

Author

Alex Ratushnyak, Mar 01 2014

Keywords

• nonn

Examples

			The two cubes nearest to 0 are 0 and 1, and, because 0+0+1 is a perfect cube, 0 is in the sequence.
The two cubes nearest to 1 are 0 and 1, and, because 1+0+1=2 is not a perfect cube, 1 is not in the sequence.
The two cubes nearest to 29 are 27 and 8, and, because 29+27+8=64=4^3 is a perfect cube, 29 is in the sequence.
		

Crossrefs

Cf. A000578, A238489.

Programs

Mathematica

pcQ[n_]:=Module[{cr=Surd[n,3]},IntegerQ[Surd[Total[Nearest[Range[ Floor[ cr]-1,Ceiling[cr]+1]^3,n,2]]+n,3]]]; Select[Range[0,520000],pcQ] (* Harvey P. Dale, Jul 25 2018 *)

Python

def icbrt(a):
    sr = 1 << (int.bit_length(int(a)) >> 1)
    while a < sr*sr*sr:  sr>>=1
    b = sr>>1
    while b:
        s = sr + b
        if a >= s*s*s:  sr = s
        b>>=1
    return sr
for k in range(1000000):
    s = icbrt(k)
    if k and s*s*s==k:  s-=1
    d1 = abs(k-s**3)
    d2 = abs(k-(s+1)**3)
    d3 = abs(k-(s-1)**3)
    kxy = k + s**3 + (s+1)**3
    if s and d3
				

Sage

def gen_a():
    n = 1
    while True:
        for t in range(n*(n*n + 3), (n+1)*(n*n + 2*n + 4) + 1):
            c = t + (2*n + 1)*(n*n + n + 1)
            if round(floor(c^(1/3)))^3 == c:
                yield t
        n += 1               # Ralf Stephan, Mar 09 2014