cp's OEIS Frontend

A338687 Number of ways to write n as x^4 + y^2 + floor(z^2/7), where x,y,z are integers with x >= 0, y >= 1 and z >= 2.

%I A338687 #19 May 07 2021 01:10:54
%S A338687 1,2,2,3,3,3,3,2,3,4,4,4,3,2,3,4,4,6,6,4,5,5,3,4,6,7,6,6,5,5,4,4,6,8,
%T A338687 2,5,10,4,5,5,7,6,5,4,7,6,2,5,6,7,5,8,8,4,5,6,6,6,3,4,9,3,4,5,6,9,8,7,
%U A338687 5,4,5,6,8,6,1,6,6,5,5,5,4,11,9,7,9,6,7,7,8,5,8,8,8,6,6,5,7,8,10,10
%N A338687 Number of ways to write n as x^4 + y^2 + floor(z^2/7), where x,y,z are integers with x >= 0, y >= 1 and z >= 2.
%C A338687 Conjecture: a(n) > 0 for all n > 0.
%C A338687 We have verified a(n) > 0 for all n = 1..5*10^6.
%C A338687 See also A338686 for a similar conjecture.
%H A338687 Zhi-Wei Sun, <a href="/A338687/b338687.txt">Table of n, a(n) for n = 1..10000</a>
%e A338687 a(1) = 1 with 1 = 0^4 + 1^2 + floor(2^2/7).
%e A338687 a(75) = 1 with 75 = 0^4 + 8^2 + floor(9^2/7).
%e A338687 a(1799) = 1 with 1799 = 5^4 + 25^2 + floor(62^2/7).
%e A338687 a(7224) = 1 with 7224 = 9^4 + 19^2 + floor(46^2/7).
%e A338687 a(27455) = 2 with 27455 = 0^4 + 7^2 + floor(438^2/7) = 8^4 + 118^2 + floor(257^2/7).
%t A338687 SQ[n_]:=SQ[n]=IntegerQ[Sqrt[n]];
%t A338687 tab={};Do[r=0;Do[If[SQ[n-x^4-Floor[y^2/7]],r=r+1],{x,0,(n-1)^(1/4)},{y,2,Sqrt[7(n-x^4)-1]}];tab=Append[tab,r],{n,1,100}];Print[tab]
%Y A338687 Cf. A000290, A000583, A270566, A338686, A338696, A343387, A343391, A343397.
%K A338687 nonn
%O A338687 1,2
%A A338687 _Zhi-Wei Sun_, Apr 23 2021