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A282093 Larger member of a pair (x,y) which solves x^2+y^2 = z^3 for positive x, y and z. 2
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 (list; graph; refs; listen; history; text; internal format)
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:

CROSSREFS

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

Sequence in context: A134948 A060045 A000462 * A032930 A033293 A231501

Adjacent sequences:  A282090 A282091 A282092 * A282094 A282095 A282096

KEYWORD

nonn

AUTHOR

R. J. Mathar, Feb 06 2017

STATUS

approved

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Last modified July 19 09:33 EDT 2019. Contains 325155 sequences. (Running on oeis4.)