A266364 - OEIS

%I #9 Dec 28 2015 09:12:26

%S 6,1,69,7,1,46,13,5,1,1,2,1,2,4,27,2,1,2,28,3,2,2,37,1,4,1,11,1,2,5,1,

%T 5,1,4,2,1,1,8,4,6,8,2,1,1,6,3,3,2,3,1,18,1,2,3,6,9,1,2,6,5,2

%N Least positive integer x such that n + x^4 = y^2 + z^3 for some positive integers y and z, or 0 if no such x exists.

%C The general conjecture in A266277 implies that for any integer m there are positive integers x, y and z such that m + x^2 = y^3 + z^4.

%C See also A266152 and A266363 for similar sequences.

%H Zhi-Wei Sun, <a href="/A266364/b266364.txt">Table of n, a(n) for n = 0..10000</a>

%e a(0) = 6 since 0 + 6^4 = 28^2 + 8^3.

%e a(2) = 69 since 2 + 69^4 = 44^2 + 283^3.

%e a(5) = 46 since 5 + 46^4 = 1742^2 + 113^3.

%e a(570) = 983 since 570 + 983^4 = 546596^2 + 8595^3.

%e a(8078) = 2255 since 8078 + 2255^4 = 1926054^2 + 28083^3.

%t SQ[n_]:=SQ[n]=IntegerQ[Sqrt[n]]

%t Do[x=1;Label[bb];Do[If[SQ[n+x^4-y^3],Print[n," ",x];Goto[aa]],{y,1,(n+x^4-1)^(1/3)}];x=x+1;Goto[bb];Label[aa];Continue,{n,0,60}]

%Y Cf. A000290, A000578, A000583, A266152, A266153, A266230, A266231, A266277, A266314, A266363.

%K nonn

%O 0,1

%A _Zhi-Wei Sun_, Dec 28 2015