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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

Table of n, a(n) for n=1..39.

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<d2:  kxy = k + s**3 + (s-1)**3

    r = icbrt(kxy)

    if r*r*r==kxy:  print(str(k), end=', ')

(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

CROSSREFS

Cf. A000578, A238489.

Sequence in context: A264530 A141910 A111032 * A033219 A142407 A183714

Adjacent sequences:  A238596 A238597 A238598 * A238600 A238601 A238602

KEYWORD

nonn

AUTHOR

Alex Ratushnyak, Mar 01 2014

STATUS

approved

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