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 A238599 Numbers k such that k+x+y is a perfect cube, where x and y are the two cubes nearest to k. 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS EXAMPLE 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. 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 *) PROG (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

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Last modified June 14 20:21 EDT 2021. Contains 345038 sequences. (Running on oeis4.)