A282093 Larger member of a pair (x,y) which solves x^2+y^2 = z^3 for positive x, y and z.

2, 10, 11, 16, 26, 30, 39, 46, 52, 54, 68, 80, 88, 100, 110, 117, 120, 128, 130, 142, 145, 170, 198, 205, 208, 222, 236, 240, 250, 270, 286, 297, 310, 312, 322, 350, 366, 368, 371, 377, 406, 414, 415, 416, 432, 455, 481, 488, 505, 518, 520, 524, 544, 549, 584

Offset

1,1

Comments

Values y such that x^2+y^2 = z^3 has a solution 1<=x<=y with integer x, y and z.

The positive values of A033431 are a subsequence, induced by solutions where x=y.

There are entries which have more than one representation, e.g., 10^2 + 198^2 = 34^3 and 107^2 + 198^2 = 37^3 both with y=198. 234^2 + 415^2 = 61^3 and 320^2 + 415^2 = 65^3 both with y=415.

The ordered sequence of x can apparently be constructed by retrieving the perfect squares in A106265 and printing their square roots: 1, 2, 5, 7, 8, 9, 10, 11, 16, 17, 18 , 26, 27, 30,...

Links

Table of n, a(n) for n=1..55.

Example

2^2+2^2=2^3, so 2 is in. 5^2+10^2=5^3, so 10 is in. 2^2+11^2 = 5^3, so 11 is in. 16^2+16^2=8^3, so 16 is in.

Maple

isA282093 := proc(y)
    local x, z3 ;
    for x from 1 to y do
        z3 := x^2+y^2 ;
        if isA000578(z3) then
            return true ;
        end if;
    end do:
    return false ;
end proc:
for y from 1 to 800 do
    if isA282093(y) then
        printf("%d, \n", y) ;
    end if;
end do:

Mathematica

isA282093[y_] := Module[{x, z3},
For[x = 1, x <= y, x++, z3 = x^2+y^2; If[IntegerQ[z3^(1/3)], Return[True]]]; Return[False]];
Reap[For[y = 1, y <= 800, y++, If[isA282093[y], Print[y]; Sow[y]]]][[2, 1]] (* Jean-François Alcover, May 29 2023, after R. J. Mathar *)

Crossrefs

Cf. A000404 (values of z), A033431, A106265.

Sequence in context: A000462 A340649 A309942 * A032930 A033293 A231501

Adjacent sequences: A282090 A282091 A282092 * A282094 A282095 A282096

Keyword

nonn

Author

R. J. Mathar, Feb 06 2017

Status

approved