A116884 Integers k such that 0 < |k^5 - m^2| <= k^(3/2) for some integer m.

1, 5, 8, 23, 27, 55, 73, 76, 377, 396, 432, 18219, 18231, 747343, 748635, 5523608, 7626590, 32866452, 82251007, 1133553044, 1778903359, 3664408636, 7208605769, 26149894782

Offset

1,2

Comments

(k, m) = (1, 0), (5, 56), (8, 181), (23, 2537), (27, 3788), (55, 22434), (73, 45531), (76, 50354), ... - Vincenzo Librandi, Mar 20 2026

Links

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

Example

|432^5 - 3878907^2| = 8217 < 432^(3/2).

Mathematica

Select[Range[1, 5*100^3], Function[k, Module[{m0=Round[Sqrt[k^5]]}, AnyTrue[Range[m0-2, m0+2], Function[m, 0<Abs[k^5-m^2]<=k^(3/2)]]]]] (* Vincenzo Librandi, Mar 20 2026 *)

Prog

(Magma) res := [1]; for k in [1..100^3] do m0 := Round(Sqrt(k^5)); ok := false;
for m in [m0-2..m0+2] do if m ne 0 and Abs(k^5 - m^2) gt 0 and Abs(k^5 - m^2) le k^(3/2) then
ok := true; break; end if; end for; if ok then Append(~res, k); end if; end for; res; // Vincenzo Librandi, Mar 20 2026

Crossrefs

Cf. A078933, A116885.

Sequence in context: A120043 A063897 A092733 * A192651 A105963 A270125

Adjacent sequences: A116881 A116882 A116883 * A116885 A116886 A116887

Keyword

nonn,more

Author

Giovanni Resta, Feb 27 2006

Status

approved