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A259836 Integers n where n^3 + (n+1)^3 is a Taxicab number A001235. 2
9, 121, 235, 301, 1090, 1293, 1524, 3152, 8010, 15556, 15934, 19247, 20244, 21498, 24015, 25363, 25556, 45462, 57872, 63758, 80016, 93349, 94701, 101929, 113098, 119942, 132414, 143653, 167147, 186540, 192629, 229508, 246122, 247318, 292154, 307534, 322870 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

David Rabahy and Alois P. Heinz and Chai Wah Wu, Table of n, a(n) for n = 1..90 (first 38 terms from David Rabahy, next 12 terms from Alois P. Heinz)

EXAMPLE

9^3 + 10^3 = 1729 = A001235(1), so 9 is in the sequence.

MAPLE

filter:= proc(n)

  local D, b, a, Q;

  D:= numtheory:-divisors(n);

  for b in D do

    a:= n/b;

    Q:= 12*b - 3*a^2;

    if Q > 9 and issqr(Q) and Q < 9*a^2 then return true fi

  od;

  false

end proc:

select(x -> filter(x^3 +(x+1)^3), [$1..100000]); # Robert Israel, Jul 07 2015

MATHEMATICA

Select[Range[10000], Length[PowersRepresentations[#^3 + (# + 1)^3, 2, 3]]==2 &] (* Vincenzo Librandi, Jul 10 2015 *)

PROG

(Python 3.x)

start = 9

end = 500000

print(start, end)

cubes = []

t = end**3+(end+1)**3

max = int(t**(1/3)+.5)

for i in range(0, max+1):

  cubes.append(i**3)

for x in range(start, end):

  t = cubes[x]+cubes[x+1]

  for i in range(1, x):

   z = t-cubes[i]

   n = int(z**(1/3)+.5)

   if cubes[n] == z:

    print(x, x+1, i, n, '\a')

(Python)

from __future__ import division

from gmpy2 import is_square

from sympy import divisors

A259836_list = []

for n in range(10000):

    m = n**3+(n+1)**3

    for x in divisors(m):

        x2 = x**2

        if x2 > m:

            break

        if x != (2*n+1) and m < x*x2 and is_square(12*m//x-3*x2):

            A259836_list.append(n)

            break # Chai Wah Wu, Jan 10 2016

CROSSREFS

Cf. A001235, A005898.

Sequence in context: A002691 A234320 A157930 * A017102 A167722 A103930

Adjacent sequences:  A259833 A259834 A259835 * A259837 A259838 A259839

KEYWORD

nonn

AUTHOR

David Rabahy, Jul 06 2015

STATUS

approved

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Last modified December 8 17:01 EST 2021. Contains 349596 sequences. (Running on oeis4.)