A122409 Numbers k such that there is no cube between k^2 and (k+1)^2.

1, 3, 4, 6, 7, 8, 9, 10, 12, 13, 15, 16, 17, 19, 20, 21, 23, 24, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35, 37, 38, 39, 40, 42, 43, 44, 45, 47, 48, 49, 50, 51, 53, 54, 55, 56, 57, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 71, 72, 73, 74, 75, 77, 78, 79, 80, 81, 83, 84, 85, 86, 87

Offset

1,2

Links

Table of n, a(n) for n=1..72.

Example

4 is a term because there is no cube between 4^2 = 16 and 5^2 = 25;
5 is not a term because between 5^2 = 25 and 6^2 = 36 there is one cube, 27.

Maple

A:={seq(x^3, x=1..90)}: a:=proc(n) if {seq(y, y=n^2+1..(n+1)^2-1)} intersect A ={} then n else fi end: seq(a(n), n=1..90); # Emeric Deutsch, Oct 25 2006

Mathematica

Sqrt[#]&/@Select[Partition[Range[100]^2, 2, 1], NoneTrue[Surd[Range[#[[1]]+ 1, #[[2]] -1], 3], IntegerQ]&][[All, 1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 30 2021 *)

Prog

(PARI) isok(n) = sum(k=n^2+1, (n+1)^2-1, ispower(k, 3)) == 0; \\ Michel Marcus, Jan 09 2019

Crossrefs

Cf. A000290 (squares), A000578 (cubes).

Sequence in context: A039130 A361780 A004712 * A039093 A085925 A107907

Adjacent sequences: A122406 A122407 A122408 * A122410 A122411 A122412

Keyword

nonn

Author

Zak Seidov, Oct 19 2006

Status

approved