cp's OEIS Frontend

A266528 Least positive integer x such that n + x^5 = y^2 + z^3 for some positive integers y and z, or 0 if no such x exists.

%I A266528 #18 Jan 05 2016 04:20:12
%S A266528 8,1,8,3,1,2,11,5,1,1,42,1,2,11,3,21,1,3,2,5,2,3,3,1,7,1,3,1,22,4,1,2,
%T A266528 1,2,8,1,1,3,5,13,2,2,1,1,2,27,3,3,2,1,2,1,7,6,3,5,1,2,7,2,5,15,1,17,
%U A266528 1,13,4,1,2,2,86
%N A266528 Least positive integer x such that n + x^5 = y^2 + z^3 for some positive integers y and z, or 0 if no such x exists.
%C A266528 By the general conjecture in A266277, for any integer m there are positive integers x, y and z such that m + x^5 = y^2 + z^3.
%H A266528 Zhi-Wei Sun, <a href="/A266528/b266528.txt">Table of n, a(n) for n = 0..1100</a>
%e A266528 a(0) = 8 since 0 + 8^5 = 104^2 + 28^3.
%e A266528 a(2) = 8 since 2 + 8^5 = 179^2 + 9^3.
%e A266528 a(6) = 11 since 6 + 11^5 = 143^2 + 52^3.
%e A266528 a(10) = 42 since 10 + 42^5 = 11415^2 + 73^3.
%e A266528 a(15) = 21 since 15 + 21^5 = 1355^2 + 131^3.
%e A266528 a(435) = 3019 since 435 + 3019^5 = 475594653^2 + 290845^3.
%t A266528 SQ[n_]:=SQ[n]=IntegerQ[Sqrt[n]]
%t A266528 Do[x=1;Label[bb];Do[If[SQ[n+x^5-y^3],Print[n," ",x];Goto[aa]],{y,1,(n+x^5-1)^(1/3)}];x=x+1;Goto[bb];Label[aa];Continue,{n,0,70}]
%Y A266528 Cf. A000290, A000578, A000584, A266152, A266153, A266212, A266215, A266230, A266231, A266277, A266314, A266363, A266364.
%K A266528 nonn
%O A266528 0,1
%A A266528 _Zhi-Wei Sun_, Dec 31 2015