A265203 - OEIS

%I #31 Nov 13 2024 12:48:02

%S 9,99,9009,14841,76167,108801,239932,828828,886688,2112112,4663664,

%T 7152517,17333371,17511571,42844824,61200216,135666531,658808856,

%U 6953443596,6961551696,27110501172,46277277264,405162261504,483867768384,522733337225,588114411885

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

%C 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

%H Chai Wah Wu, <a href="/A265203/b265203.txt">Table of n, a(n) for n = 1..46</a> (all terms < 2000000300000030000001)

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

%p ispali:= proc(n) local L; L:= convert(n,base,10);

%p   ListTools:-Reverse(L) = L end proc:

%p A265203:= proc(N) # get all terms <= N

%p   local S,a,b,t;

%p   S:= select(t -> t<=N and ispali(t),

%p      {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)});

%p   sort(convert(S,list));

%p end proc:

%p A265203(10^9); # _Robert Israel_, Dec 07 2015

%t 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 *)

%o (Sage)

%o def palindromic_cubic_sums(x_max):

%o     success = set()

%o     for x_min in range(1,x_max^(1/3)):

%o         sum_powers = x_min^3

%o         for i in range(x_min+1,x_max^(1/3)):

%o             sum_powers += (i^3)

%o             if sum_powers >= x_max:

%o                 break

%o             if str(sum_powers) == str(sum_powers)[::-1]:

%o                 success.add(sum_powers)

%o     return sorted(success)

%Y Cf. A002113, A217843.

%K nonn,base

%O 1,1

%A _Ann Marie Murray_, Dec 03 2015