cp's OEIS Frontend

A266363 Least positive integer x such that n + x^2 = y^3 + z^4 for some positive integers y and z, or 0 if no such x exists.

%I A266363 #12 Dec 30 2015 03:37:29
%S A266363 3,1,302,5,47,2,362,6,1,372,14,61,4,2,70,3,1,24,5,3,2,14,364,1,2,8,10,
%T A266363 1,454,6,848,7,15,7,3,18,14,13,1362,2,5,10,1,37,6,9,6,68,13,4,24,36,
%U A266363 37,6,26,5,3,5,15,7,9
%N A266363 Least positive integer x such that n + x^2 = y^3 + z^4 for some positive integers y and z, or 0 if no such x exists.
%C A266363 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 A266363 See also A266152 and A266364 for similar sequences.
%H A266363 Zhi-Wei Sun, <a href="/A266363/b266363.txt">Table of n, a(n) for n = 0..10000</a>
%e A266363 a(0) = 3 since 0 + 3^2 = 2^3 + 1^4.
%e A266363 a(2) = 302 since 2 + 302^2 = 45^3 + 3^4.
%e A266363 a(3) = 5 since 3 + 5^2 = 3^3 + 1^4.
%e A266363 a(38) = 1362 since 38 + 1362^2 = 121^3 + 17^4.
%e A266363 a(394) = 110307 since 394 + 110307^2 = 2283^3 + 128^4.
%e A266363 a(5546) = 945840 since 5546 + 945840^2 = 9625^3 + 233^4.
%t A266363 CQ[n_]:=CQ[n]=IntegerQ[n^(1/3)]
%t A266363 Do[x=1;Label[bb];Do[If[CQ[n+x^2-y^4],Print[n," ",x];Goto[aa]],{y,1,(n+x^2-1)^(1/4)}];x=x+1;Goto[bb];Label[aa];Continue,{n,0,60}]
%Y A266363 Cf. A000290, A000578, A000583, A266152, A266153, A266230, A266231, A266277, A266314, A266364.
%K A266363 nonn
%O A266363 0,1
%A A266363 _Zhi-Wei Sun_, Dec 28 2015