[seqfan] Re: n^3 - (largest square < n^3)

[Maximilian Hasler]

See

A087285  	 	 Possible differences between a cube and the next smaller square.
	2, 4, 7, 11, 13, 15, 19, 20, 26, 28, 35, 39, 40, 45, 47, 48, 49, 53,
55, 56, 60, 63, 67, 74, 76, 79, 81, 83, 100, 104, 107, 109, 116, 127,
135, 139, 146, 147, 148, 150, 152, 155, 170, 174, 180, 184, 186, 191,
193, 200, 207, 212, 215, 216, 233, 235, 242, 244, 249 (list; graph;
listen)

Maximilian


On Mon, Jan 5, 2009 at 12:55 PM, zak seidov <zakseidov at yahoo.com> wrote:
> Dear seqfans,
>
> There are 158 possible non-zero values of difference
> [n^3 - (largest square < n^3)] less than 1000:
>
> 2, 4, 7, 11, 13, 19, 20, 26, 28, 35, 39, 40, 45, 47, 48, 49, 53, 55, 56, 60, 63, 67, 74, 76, 79, 81, 83, 100, 104, 107, 109, 116, 135, 139, 146, 147, 148, 150, 152, 155, 170, 174, 180, 184, 186, 191, 193, 200, 207, 212, 215, 216, 233, 235, 242, 244, 249, 251, 270, 277, 292, 293, 299, 301, 307, 308, 343, 355, 362, 364, 366, 368, 371, 391, 405, 424, 431, 433, 440, 448, 455, 459, 464, 471, 476, 496, 499, 503, 506, 508, 511, 515, 516, 524, 535, 546, 580, 586, 587, 589, 593, 596, 615, 622, 631, 639, 648, 652, 663, 667, 674, 676, 680, 683, 702, 703, 704, 726, 728, 732, 735, 755, 760, 764, 766, 767, 769, 775, 776, 782, 802, 804, 828, 831, 832, 847, 856, 859, 866, 868, 875, 888, 895, 900, 908, 914, 944, 945, 954, 964, 971, 973, 975, 980, 984, 991, 996, 999.
>
> What about filling gaps in this list
> (finding more terms < 1000)?
> thx, zak
>
> For n <~10^8 there are 207 values of n for which
> 0<[n^3 - (largest square < n^3)]<1000, see
> http://zak08.livejournal.com/3376.html
> n^3 - (largest square < n^3)
>
> Cf. A077116  n^3 - A065733 (n),
> A065733  Largest square <= n^3.
>
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