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%I #16 Jun 08 2019 17:55:54
%S 1,64,68,120,729,4096,15625,46656,117649,262144,531441,1000000,
%T 1771561,2985984,4826809,7529536,11390625,16777216,24137569,34012224,
%U 47045881,64000000,85766121,113379904
%N Numbers k such that the smallest integer value >= 0 of the form x^3 - k^2 equals the smallest integer value >= 0 of the form x^2 - k^3.
%C If k is power of 6 (k is in A001014), k is in the sequence, but there are also values of other forms; e.g., 68 = 2^2*17.
%F Numbers k such that ceiling(k^(2/3))^3 - k^2 = ceiling(k^(3/2))^2 - k^3.
%F Conjectures from _Colin Barker_, Jun 29 2017: (Start)
%F G.f.: x*(1 + 57*x - 359*x^2 + 953*x^3 - 888*x^4 + 1352*x^5 - 895*x^6 + 1001*x^7 - 771*x^8 + 325*x^9 - 56*x^10) / (1 - x)^7.
%F a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n > 11.
%F (End)
%t Do[ If[ Ceiling[n^(3/2)]^2 + n^2 == Ceiling[n^(2/3)]^3 + n^3, Print[n]], {n, 1, 5*10^6}]
%o (PARI) for(n=1,130000,if(ceil(n^(3/2))^2-n^3==ceil(n^(2/3))^3-n^2,print1(n,",")))
%K nonn
%O 1,2
%A _Benoit Cloitre_, May 20 2002
%E More terms from _Robert G. Wilson v_, May 27 2002
%E More terms from Lambert Klasen (lambert.klasen(AT)gmx.de), Dec 23 2004
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