A265203 Palindromes that can be written as the sum of two or more consecutive positive cubes.

9, 99, 9009, 14841, 76167, 108801, 239932, 828828, 886688, 2112112, 4663664, 7152517, 17333371, 17511571, 42844824, 61200216, 135666531, 658808856, 6953443596, 6961551696, 27110501172, 46277277264, 405162261504, 483867768384, 522733337225, 588114411885

Offset

1,1

Comments

Can any term in the sequence be written as sum of 2 or more consecutive cubes in more than one way? The answer is no for a(1)-a(46). - Chai Wah Wu, Dec 17 2015

Links

Chai Wah Wu, Table of n, a(n) for n = 1..46 (all terms < 2000000300000030000001)

Example

14841 can be written as 16^3 + 17^3 + 18^3.

Maple

ispali:= proc(n) local L; L:= convert(n, base, 10);
  ListTools:-Reverse(L) = L end proc:
A265203:= proc(N) # get all terms <= N
  local S, a, b, t;
  S:= select(t -> t<=N and ispali(t),
     {seq(seq(b^2*(b+1)^2/4 - a^2*(a+1)^2/4, a=0..b-2), b=2..(1+iroot(4*N, 3))/2)});
  sort(convert(S, list));
end proc:
A265203(10^9); # Robert Israel, Dec 07 2015

Mathematica

lim = 800; Sort@ Select[Plus @@@ Map[#^3 &, Select[Flatten[Table[Partition[Range@ lim, k, 1], {k, 2, lim}], 1], Times @@ Differences@ # == 1 &]], # == Reverse@ # &@ IntegerDigits@ # &] (* Michael De Vlieger, Dec 16 2015 *)

Prog

(Sage)
def palindromic_cubic_sums(x_max):
    success = set()
for x_min in range(1, x_max^(1/3)):
        sum_powers = x_min^3
for i in range(x_min+1, x_max^(1/3)):
            sum_powers += (i^3)
            if sum_powers >= x_max:
                break
            if str(sum_powers) == str(sum_powers)[::-1]:
                success.add(sum_powers)
    return sorted(success)

Crossrefs

Cf. A002113, A217843.

Sequence in context: A035027 A196487 A262540 * A078238 A080494 A077710

Adjacent sequences: A265200 A265201 A265202 * A265204 A265205 A265206

Keyword

nonn,base

Author

Ann Marie Murray, Dec 03 2015

Status

approved