A259836 Integers n where n^3 + (n+1)^3 is a Taxicab number A001235.

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

Offset: 1

Author

David Rabahy, Jul 06 2015

Keywords

• nonn

Examples

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

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)

Crossrefs

Cf. A001235, A005898.

Programs

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 *)

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