cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

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

Original entry on oeis.org

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
Offset: 1

Views

Author

Giovanni Resta, Jan 15 2006

Keywords

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

Crossrefs

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

Programs

  • 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)

Extensions

Definition corrected by Giovanni Resta, Aug 17 2011

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.

Original entry on oeis.org

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

Views

Author

Zhi-Wei Sun, Apr 14 2020

Keywords

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

Crossrefs

Cf. A000217, A000583, A115160, A306227, A334086.

Programs

  • 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]
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.