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A282095
Larger member of a coprime pair (x,y) which solves x^2 + y^2 = z^3 with positive x, y and z.
1
11, 46, 52, 117, 142, 198, 236, 286, 415, 488, 524, 549, 621, 666, 835, 873, 908, 970, 1001, 1199, 1388, 1432, 1692, 1757, 1962, 1964, 1971, 2035, 2041, 2366, 2392, 2630, 2655, 2681, 2702, 2815, 2826, 3195, 3421, 3544, 3664, 3715, 4048, 4070, 4097, 4356
OFFSET
1,1
COMMENTS
If x and y are coprime, so obviously are also (x,z) and (y,z).
The ordered values of the bases of the cubes, z, are a subsequence of (and conjecturally the same as) A008846.
For production purposes we advice to use the parametrized representations (see references).
LINKS
Imin Chen, On the equation s^2+y^(2p)=alpha^3, Math. Comp. 77 (262) (2008) 1223-1227.
Sander R. Dahmen, A refined modular approach to the diophantine equation x^2+y^(2n)=z^3, arXiv:1002.0020 [math.NT] (2010).
FORMULA
{y: x^2 + y^2 = z^3; gcd(x,y) = 1; 1 <= x <= y; x, y, z in N}
EXAMPLE
2^2 + 11^2 = 5^3, so 11 is in the sequence.
9^2 + 46^2 = 13^3, so 46 is in the sequence.
47^2 + 52^2 = 17^3, so 52 is in the sequence.
44^2 + 117^2 = 25^2, so 117 is in the sequence.
MAPLE
# slow version for demonstration only.
isA282095 := proc(y)
local x, z3 ;
for x from 1 to y do
if igcd(x, y) = 1 then
z3 := x^2+y^2 ;
if isA000578(z3) then
return true ;
end if;
end if;
end do:
return false ;
end proc:
for y from 1 do
if isA282095(y) then
printf("%d, \n", y) ;
end if;
end do:
MATHEMATICA
okQ[y_] := Module[{x, z3}, For[x=1, x<y, x++, If[CoprimeQ[x, y], z3 = x^2 + y^2; If[IntegerQ[z3^(1/3)], Print[y]; Return[True]]]]; Return[False]];
Select[Range[5000], okQ] (* Jean-François Alcover, Dec 04 2017, after R. J. Mathar *)
CROSSREFS
Subsequence of A282093. Cf. A099533.
Sequence in context: A322560 A110114 A116193 * A063158 A081587 A377663
KEYWORD
nonn
AUTHOR
R. J. Mathar, Feb 06 2017
STATUS
approved