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.

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.

Links

Table of n, a(n) for n=1..24.

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