A175610 Numbers k such that k^4 = x^4 + y^4 + z^4, where x,y,z are positive integers.
422481, 844962, 1267443, 1689924, 2112405, 2534886, 2813001, 2957367, 3379848, 3802329, 4224810, 4647291, 5069772, 5492253, 5626002, 5914734, 6337215, 6759696, 7182177, 7604658, 8027139, 8439003, 8449620, 8707481, 8872101, 9294582, 9717063, 10139544, 10562025, 10984506
Offset: 1
Keywords
Examples
a(1) = 422481 because 422481^4 = 95800^4 + 217519^4 + 414560^4. a(61) = 20615673 because 20615673^4 = 2682440^4 + 15365639^4 + 18796760^4.
Links
- Charles R Greathouse IV, Table of n, a(n) for n = 1..4999
Programs
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Mathematica
Select[Range[100], (p = PowersRepresentations[#^4, 3, 4]; (Select[p, #[[1]] > 0 && #[[2]] > 0 && #[[3]] > 0 &] != {})) &] (* Jinyuan Wang, Feb 20 2020 *) -
PARI
is(n) = for(a=sqrtnint(n^4\3,4), n-1, for(b=1, a, for(c=1, b, if(n^4==a^4+b^4+c^4, return(1))))); 0; \\ Charles R Greathouse IV, Aug 29 2013 and slightly modified by Jinyuan Wang, Feb 20 2020
Extensions
Terms and example corrected by Charles R Greathouse IV, Aug 29 2013
First 0 removed by Jinyuan Wang, Feb 20 2020
Comments