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 A265203 Palindromes that can be written as the sum of two or more consecutive positive cubes. 1
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified June 8 00:26 EDT 2023. Contains 363157 sequences. (Running on oeis4.)