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 1-5 of 5 results.

A115160 Numbers that are not the sum of two triangular numbers and a fourth power.

Original entry on oeis.org

33, 63, 75, 125, 365, 489, 492, 684, 693, 723, 954, 1043, 1185, 1505, 1623, 1629, 1736, 1775, 1899, 1904, 1925, 2015, 2051, 2679, 2883, 3534, 3774, 3936, 4332, 4461, 4739, 4923, 5445, 5721, 5847, 6285, 6348, 6474, 6783, 7034, 7478, 8604, 9576, 9686, 9863
Offset: 1

Views

Author

Giovanni Resta, Jan 15 2006

Keywords

Comments

There are 88 such numbers up to 2*10^9, the last one in this range being 1945428.

Links

Crossrefs

Cf. A022552, A014158, A115159, A115161, A115162, A115163.

Programs

  • PARI
    sumset_lim(a,b,lim)=my(v=[],u,t);if(a==b,for(i=1,#a,u=List();for(j=i,#b,t=a[i]+b[j];if(t>lim,break);listput(u,t));v=vecsort(concat(v,Vec(u)),,8)),for(i=1,#a,u=List();for(j=1,#b,t=a[i]+b[j];if(t>lim,break);listput(u,t));v=vecsort(concat(v,Vec(u)),,8)));v
makev(lim)=my(n=floor(sqrt(2*lim)-1/2),v);sumset_lim(v=vector(n,k,k*(k-1)/2),v,lim)
is(n)=for(i=1,#v,if(ispower(n-v[i],4),return(0));if(v[i]>n,return(1)))
v=makev(1e5);
for(n=1,1e5,if(is(n),print1(n", "))) \\ Charles R Greathouse IV, Aug 17 2011

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

A115161 Numbers that are not the sum of a triangular number, a nonnegative cube and a fourth power.

Original entry on oeis.org

13, 35, 40, 41, 50, 51, 59, 76, 77, 112, 124, 139, 149, 150, 157, 165, 168, 175, 176, 178, 182, 183, 189, 193, 197, 205, 208, 215, 224, 229, 241, 243, 249, 273, 288, 305, 306, 314, 329, 332, 366, 373, 383, 397, 412, 413, 418, 420, 429, 438, 453, 455, 457, 461
Offset: 1

Views

Author

Giovanni Resta, Jan 15 2006

Keywords

Comments

There are 15682461 such numbers up to 10^9, the last one in this range being 999999923.

Crossrefs

Cf. A022552, A014158, A115159, A115160, A115162, A115163.

A115163 Numbers that are not the sum of two triangular numbers and a nonnegative cube.

Original entry on oeis.org

41, 104, 188, 923
Offset: 1

Views

Author

Giovanni Resta, Jan 15 2006

Keywords

Comments

Probably finite. No other terms up to 10^9.

Crossrefs

Cf. A022552, A014158, A115159, A115160, A115161, A115162.

A260411 Number of ways n can be represented as a sum of a positive cube, a positive square, and a positive triangular number.

Original entry on oeis.org

0, 0, 0, 1, 0, 1, 1, 0, 2, 0, 1, 2, 2, 2, 0, 3, 1, 1, 3, 1, 4, 0, 1, 3, 1, 2, 1, 5, 0, 2, 3, 2, 4, 2, 4, 0, 2, 3, 6, 3, 2, 3, 1, 3, 1, 5, 4, 4, 2, 2, 2, 2, 3, 5, 4, 2, 2, 3, 4, 2, 4, 1, 4, 1, 5, 4, 3, 4, 3, 4, 0, 7, 5, 5, 2, 4, 3, 1, 7, 4, 5, 3, 3, 8, 1, 2, 6, 2, 6, 2, 5
Offset: 0

Views

Author

Alex Ratushnyak, Jul 24 2015

Keywords

Comments

Indices of zeros: A115162.
It appears that there are 14 zeros and 33 ones. Conjecture: every integer appears in the sequence finitely many times.

Examples

			8 = 1 + 1 + 6 = 1 + 4 + 3, two representations, so a(8)=2.

Crossrefs

Cf. A115162.
Showing 1-5 of 5 results.

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