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.

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

Offset

1,1

Comments

Conjecture: The sequence only has 602 terms as listed in the b-file.

Our computation indicates that after the 602-th 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

Zhi-Wei Sun, Table of n, a(n) for n = 1..602

Zhi-Wei Sun, Mixed sums of squares and triangular numbers, Acta Arith. 127(2007), 103-113.

Mathematica

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

Zhi-Wei Sun, Apr 14 2020

Status

approved