cp's OEIS Frontend

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

%I A265203 #31 Nov 13 2024 12:48:02
%S A265203 9,99,9009,14841,76167,108801,239932,828828,886688,2112112,4663664,
%T A265203 7152517,17333371,17511571,42844824,61200216,135666531,658808856,
%U A265203 6953443596,6961551696,27110501172,46277277264,405162261504,483867768384,522733337225,588114411885
%N A265203 Palindromes that can be written as the sum of two or more consecutive positive cubes.
%C A265203 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 A265203 Chai Wah Wu, <a href="/A265203/b265203.txt">Table of n, a(n) for n = 1..46</a> (all terms < 2000000300000030000001)
%e A265203 14841 can be written as 16^3 + 17^3 + 18^3.
%p A265203 ispali:= proc(n) local L; L:= convert(n,base,10);
%p A265203   ListTools:-Reverse(L) = L end proc:
%p A265203 A265203:= proc(N) # get all terms <= N
%p A265203   local S,a,b,t;
%p A265203   S:= select(t -> t<=N and ispali(t),
%p A265203      {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 A265203   sort(convert(S,list));
%p A265203 end proc:
%p A265203 A265203(10^9); # _Robert Israel_, Dec 07 2015
%t A265203 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 A265203 (Sage)
%o A265203 def palindromic_cubic_sums(x_max):
%o A265203     success = set()
%o A265203     for x_min in range(1,x_max^(1/3)):
%o A265203         sum_powers = x_min^3
%o A265203         for i in range(x_min+1,x_max^(1/3)):
%o A265203             sum_powers += (i^3)
%o A265203             if sum_powers >= x_max:
%o A265203                 break
%o A265203             if str(sum_powers) == str(sum_powers)[::-1]:
%o A265203                 success.add(sum_powers)
%o A265203     return sorted(success)
%Y A265203 Cf. A002113, A217843.
%K A265203 nonn,base
%O A265203 1,1
%A A265203 _Ann Marie Murray_, Dec 03 2015