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%I #17 Feb 24 2020 04:23:42
%S 422481,844962,1267443,1689924,2112405,2534886,2813001,2957367,
%T 3379848,3802329,4224810,4647291,5069772,5492253,5626002,5914734,
%U 6337215,6759696,7182177,7604658,8027139,8439003,8449620,8707481,8872101,9294582,9717063,10139544,10562025,10984506
%N Numbers k such that k^4 = x^4 + y^4 + z^4, where x,y,z are positive integers.
%C Main sequence is A003828.
%H Charles R Greathouse IV, <a href="/A175610/b175610.txt">Table of n, a(n) for n = 1..4999</a>
%e a(1) = 422481 because 422481^4 = 95800^4 + 217519^4 + 414560^4.
%e a(61) = 20615673 because 20615673^4 = 2682440^4 + 15365639^4 + 18796760^4.
%t Select[Range[100], (p = PowersRepresentations[#^4, 3, 4]; (Select[p, #[[1]] > 0 && #[[2]] > 0 && #[[3]] > 0 &] != {})) &] (* _Jinyuan Wang_, Feb 20 2020 *)
%o (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
%Y Cf. A003337, A003828, A175598.
%K nonn
%O 1,1
%A _Juri-Stepan Gerasimov_, Jul 24 2010
%E Terms and example corrected by _Charles R Greathouse IV_, Aug 29 2013
%E First 0 removed by _Jinyuan Wang_, Feb 20 2020
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