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
Examples
14841 can be written as 16^3 + 17^3 + 18^3.
Links
- Chai Wah Wu, Table of n, a(n) for n = 1..46 (all terms < 2000000300000030000001)
Programs
-
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
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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 *) -
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)
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