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A115159 Numbers that are not the sum of a triangular number, a square and a fourth power. 5


%S 34,63,89,99,139,164,174,193,204,245,314,399,424,454,464,489,504,524,

%T 549,714,1049,1149,1174,1439,1504,1539,1639,1799,1814,1919,2164,2239,

%U 2313,2374,2414,2439,2764,2789,3079,3319,3414,3669,3774,3814,4019,4114

%N Numbers that are not the sum of a triangular number, a square and a fourth power.

%C There are 718 such numbers up to 2*10^9, the last one in this range being 99570649.

%C It is known that each natural number can be written as the sum of two squares and a triangular number. I believe that the sequence only has 718 terms as found by __Giovanni Resta_ and listed in the b-file. - _Zhi-Wei Sun_, Apr 15 2020

%H Zhi-Wei Sun, <a href="/A115159/b115159.txt">Table of n, a(n) for n = 1..718</a>

%H Zhi-Wei Sun, <a href="http://dx.doi.org/10.4064/aa127-2-1">Mixed sums of squares and triangular numbers</a>, Acta Arith. 127(2007), 103-113.

%t TQ[n_]:=TQ[n]=IntegerQ[Sqrt[8n+1]];

%t tab={};Do[Do[If[TQ[n-x^4-y^2],Goto[aa]],{x,0,n^(1/4)},{y,0,Sqrt[n-x^4]}];tab=Append[tab,n];Label[aa],{n,0,4114}];Print[tab] (From _Zhi-Wei Sun_)

%Y Cf. A022552, A014158, A115160, A115161, A115162, A115163, A262959, A334086, A334113.

%K nonn

%O 1,1

%A _Giovanni Resta_, Jan 15 2006

%E Definition corrected by _Giovanni Resta_, Aug 17 2011

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Last modified November 26 03:20 EST 2020. Contains 338632 sequences. (Running on oeis4.)