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
KEYWORD
nonn,base
AUTHOR
Ann Marie Murray, Dec 03 2015
STATUS
approved