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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 (list; graph; refs; listen; history; text; internal format)
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 b-file. - Zhi-Wei Sun, Apr 15 2020
LINKS
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-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)
CROSSREFS
Sequence in context: A259945 A303239 A280931 * A125192 A039381 A043204
KEYWORD
nonn
AUTHOR
Giovanni Resta, Jan 15 2006
EXTENSIONS
Definition corrected by Giovanni Resta, Aug 17 2011
STATUS
approved

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Last modified July 13 04:46 EDT 2024. Contains 374267 sequences. (Running on oeis4.)