

A115159


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


5



34, 63, 89, 99, 139, 164, 174, 193, 204, 245, 314, 399, 424, 454, 464, 489, 504, 524, 549, 714, 1049, 1149, 1174, 1439, 1504, 1539, 1639, 1799, 1814, 1919, 2164, 2239, 2313, 2374, 2414, 2439, 2764, 2789, 3079, 3319, 3414, 3669, 3774, 3814, 4019, 4114
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OFFSET

1,1


COMMENTS

There are 718 such numbers up to 2*10^9, the last one in this range being 99570649.
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 bfile.  ZhiWei Sun, Apr 15 2020


LINKS

ZhiWei Sun, Table of n, a(n) for n = 1..718
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[nx^4y^2], Goto[aa]], {x, 0, n^(1/4)}, {y, 0, Sqrt[nx^4]}]; tab=Append[tab, n]; Label[aa], {n, 0, 4114}]; Print[tab] (From ZhiWei Sun)


CROSSREFS

Cf. A022552, A014158, A115160, A115161, A115162, A115163, A262959, A334086, A334113.
Sequence in context: A259945 A303239 A280931 * A125192 A039381 A043204
Adjacent sequences: A115156 A115157 A115158 * A115160 A115161 A115162


KEYWORD

nonn


AUTHOR

Giovanni Resta, Jan 15 2006


EXTENSIONS

Definition corrected by Giovanni Resta, Aug 17 2011


STATUS

approved



