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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.)