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%I #31 Jan 17 2024 15:03:39
%S 0,1,64,125,216,729,13824,15625,117649,132651,421875,438976,970299,
%T 1953125,15438249,15813251,52734375,53157376,124251499,125751501,
%U 242970624,244140625,420189749,423564751,669921875,997002999,1948441249,52776573751,83740234375
%N Cubes whose final digits are the cube root.
%D Philip Carter & Ken Russell, Problem 31, p. 86, The Complete Book of Fun Maths, John Wiley, 2004.
%F a(n) = A033819(n)^3.
%e 6 * 6 * 6 = 216, which has "6" as rightmost digit.
%t Select[Range[0,100]^3,Mod[#,10]==Surd[#,3]||Mod[#,100]==Surd[#,3]&] (* _Harvey P. Dale_, Mar 03 2023 *)
%o (PARI) apply(x->x^3,select(x -> (x^3 - x) % 10^(#digits(x)) == 0, [0..99])) \\ _David A. Corneth_, Feb 11 2020
%Y Cf. A000578, A033819.
%K nonn,base,easy
%O 1,3
%A _Jonathan Vos Post_, Aug 16 2012
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