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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
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.
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
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