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A122409
Numbers k such that there is no cube between k^2 and (k+1)^2.
0
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
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: A361780 A004712 A375740 * A039093 A085925 A107907
KEYWORD
nonn
AUTHOR
Zak Seidov, Oct 19 2006
STATUS
approved