

A334113


Positive numbers not of the form 4*x^4 + y*(y+1)/2 + z*(z+1)/2, where x,y,z are nonnegative integers.


3



23, 44, 54, 63, 117, 138, 149, 162, 180, 188, 243, 251, 261, 270, 287, 294, 398, 401, 458, 512, 611, 657, 684, 693, 734, 797, 842, 863, 914, 932, 936, 945, 987, 1029, 1047, 1098, 1323, 1401, 1449, 1472, 1484, 1494, 1574, 1608, 1637, 1769, 1792, 1799, 1823, 1839, 1902, 1995
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OFFSET

1,1


COMMENTS

Conjecture: The sequence only has 602 terms as listed in the bfile.
Our computation indicates that after the 602th term 31737789 there are no other terms below 10^8.
It is known that each n = 0,1,2,... can be written as the sum of an even square and two triangular numbers.


LINKS

ZhiWei Sun, Table of n, a(n) for n = 1..602
ZhiWei Sun, Mixed sums of squares and triangular numbers, Acta Arith. 127(2007), 103113.


MATHEMATICA

TQ[n_]:=TQ[n]=IntegerQ[Sqrt[8n+1]];
tab={}; Do[Do[If[TQ[n4x^4y(y+1)/2], Goto[aa]], {x, 0, (n/4)^(1/4)}, {y, 0, (Sqrt[4(n4x^4)+1]1)/2}]; tab=Append[tab, n]; Label[aa], {n, 0, 2000}]; Print[tab]


CROSSREFS

Cf. A000217, A000583, A115160, A306227, A334086.
Sequence in context: A168439 A332399 A198949 * A214891 A003859 A058545
Adjacent sequences: A334110 A334111 A334112 * A334114 A334115 A334116


KEYWORD

nonn


AUTHOR

ZhiWei Sun, Apr 14 2020


STATUS

approved



