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 A070931 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. 0
 1, 64, 68, 120, 729, 4096, 15625, 46656, 117649, 262144, 531441, 1000000, 1771561, 2985984, 4826809, 7529536, 11390625, 16777216, 24137569, 34012224, 47045881, 64000000, 85766121, 113379904 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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. LINKS FORMULA Numbers k such that ceiling(k^(2/3))^3 - k^2 = ceiling(k^(3/2))^2 - k^3. Conjectures from Colin Barker, Jun 29 2017: (Start) 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. 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. (End) MATHEMATICA Do[ If[ Ceiling[n^(3/2)]^2 + n^2 == Ceiling[n^(2/3)]^3 + n^3, Print[n]], {n, 1, 5*10^6}] PROG (PARI) for(n=1, 130000, if(ceil(n^(3/2))^2-n^3==ceil(n^(2/3))^3-n^2, print1(n, ", "))) CROSSREFS Sequence in context: A217846 A135124 A223590 * A095533 A044864 A162528 Adjacent sequences:  A070928 A070929 A070930 * A070932 A070933 A070934 KEYWORD nonn AUTHOR Benoit Cloitre, May 20 2002 EXTENSIONS More terms from Robert G. Wilson v, May 27 2002 More terms from Lambert Klasen (lambert.klasen(AT)gmx.de), Dec 23 2004 STATUS approved

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Last modified August 20 01:14 EDT 2019. Contains 326136 sequences. (Running on oeis4.)