A266212 Positive integers x such that x^3 = y^4 + z^2 for some positive integers y and z.
8, 13, 20, 25, 40, 125, 128, 193, 200, 208, 225, 313, 320, 328, 400, 500, 605, 640, 648, 1000, 1053, 1156, 1521, 1620, 1625, 1681, 1700, 2000, 2025, 2048, 2125, 2465, 2493, 2873, 2920, 3025, 3088, 3185, 3200, 3240, 3328, 3400, 3600, 3656, 3748, 3816, 4225, 4625, 4913, 5000, 5008, 5120, 5248, 6400, 6728, 6760, 6793, 6845, 7225, 8000
Offset: 1
Keywords
Examples
a(1) = 8 since 8^3 = 4^4 + 16^2. a(2) = 13 since 13^3 = 3^4 + 46^2. a(3) = 20 since 20^3 = 4^4 + 88^2. a(8) = 193 since 193^3 = 6^4 + 2681^2. a(12) = 313 since 313^3 = 66^4 + 3419^2. a(20) = 1000 since 1000^3 = 100^4 + 30000^2.
Links
- Zhi-Wei Sun and Chai Wah Wu, Table of n, a(n) for n = 1..698 n = 1..100 from Zhi-Wei Sun
- Zhi-Wei Sun, New conjectures on representations of integers (I), Nanjing Univ. J. Math. Biquarterly 34(2017), no. 2, 97-120.
Programs
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Mathematica
SQ[n_]:=SQ[n]=n>0&&IntegerQ[Sqrt[n]] n=0;Do[Do[If[SQ[x^3-y^4],n=n+1;Print[n," ",x];Goto[aa]],{y,1,x^(3/4)}];Label[aa];Continue,{x,1,8000}]
Comments