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.

A165291 Complement of A165289.

Original entry on oeis.org

2, 4, 5, 6, 7, 10, 11, 13, 14, 16, 20, 21, 23, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 39, 41, 42, 43, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 56, 58, 59, 60, 61, 62, 63, 66, 67, 69, 70, 72, 74, 75, 76, 77, 78, 81, 82, 83, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 99, 102
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Sep 13 2009

Keywords

Comments

Numbers which are impossible values for the difference of a square minus the nearest smaller or equal cube.

Crossrefs

Cf. A165288, A165289, A165290

Programs

  • Mathematica
    lst={};Do[a=(x=n^2)-(y=Floor[(n^2)^(1/3)]^3);If[a<=416,AppendTo[lst,a]], {n,8!}];Take[Union@lst,100]; lst1={};Do[AppendTo[lst1,n],{n,416}]; lst1; Complement[lst1,lst]

Extensions

Definition simplified - R. J. Mathar, Sep 21 2009

A152412 Nonnegative numbers of the form s^2-m^5, m>=1.

Original entry on oeis.org

0, 3, 4, 8, 11, 13, 15, 17, 24, 26, 32, 35, 37, 46, 48, 49, 63, 65, 68, 80, 81, 89, 93, 99, 112, 118, 120, 124, 132, 137, 143, 145, 157, 164, 168, 169, 193, 195, 198, 201, 224, 239, 241, 255, 257, 272, 286, 288, 292, 323, 324, 329, 333, 340, 345, 354, 356, 360, 368, 382, 399, 409, 420, 433, 440, 452, 475, 483, 486, 487, 489, 497
Offset: 1

Views

Author

N. J. A. Sloane, Oct 24 2009, based on email from Joerg Arndt, Oct 10 2009

Keywords

Crossrefs

Cf. A087286, A165289, A152411.

Programs

  • PARI
    for(k=0, 500, for(n=1, 10^5, t=n^5+k; if(issquare(t), print1(k, ", "); break()) ) );

Extensions

More terms from Zak Seidov, Oct 24 2009
Definition edited by R. J. Mathar, Mar 12 2010

A087286 Possible differences between a square and the closest smaller cube.

Original entry on oeis.org

1, 3, 8, 9, 12, 15, 17, 18, 19, 22, 24, 30, 36, 37, 38, 40, 44, 55, 57, 64, 65, 68, 71, 73, 79, 80, 89, 97, 98, 100, 101, 106, 107, 108, 112, 113, 119, 121, 128, 129, 138, 141, 145, 148, 151, 154, 156, 161, 163, 164, 168, 169, 171, 172, 190, 196, 197, 198, 204, 208
Offset: 1

Views

Author

Hugo Pfoertner, Sep 18 2003

Keywords

Comments

Integers of the form m^2 - floor((m^2-1)^(1/3))^3 for integer m.

Examples

			2^2-1^3=3, 3^2-2^3=1, 4^2-2^3=8, 5^2-2^3=17, 6^2-3^3=9, 7^2-3^3=22,...,
1138^2-109^3=15

Links

Crossrefs

Cf. A087285, A088017, A054504, A165289.

A152411 Nonnegative integers representable as m^2 - n^4 for positive integers m,n.

Original entry on oeis.org

0, 3, 8, 9, 15, 19, 20, 24, 33, 35, 40, 48, 51, 63, 65, 68, 73, 80, 84, 88, 99, 104, 105, 115, 120, 128, 129, 143, 144, 148, 153, 159, 163, 168, 175, 180, 185, 195, 200, 201, 208, 209, 216, 224, 225, 228, 240, 243, 255, 260, 273, 275, 280, 288, 289, 303, 304, 308, 319, 320
Offset: 1

Views

Author

N. J. A. Sloane, Oct 24 2009, based on email from Joerg Arndt, Oct 10 2009

Keywords

Comments

Nonnegative integers representable as the product u*v with (u-v)/2 being a positive square.

Links

Crossrefs

Cf. A087286, A165289, A152412.

Programs

  • Maple
    filter:= proc(x) local d,u;
  d:= select(t -> t^2 > x, numtheory:-divisors(x));
  for u in d do if issqr((u-x/u)/2) then return true fi od;
  false
end proc:
filter(0):= true:
select(filter, [$0..1000]); # Robert Israel, Nov 06 2017
  • Mathematica
    filterQ[x_] := Catch[With[{d = Select[Divisors[x], #^2 > x&]}, Do[If[IntegerQ[Sqrt[(u-x/u)/2]], Throw[True]], {u, d}]; Throw[False]]];
filterQ[0] = True;
Select[Range[0, 1000], filterQ] (* Jean-François Alcover, Jul 24 2020, after Robert Israel *)
  • PARI
    for(k=1,1000, fordiv(k,d, if(d*d>=k,break); if( issquare((k\d - d)/2), print1(k,", "); break) ) )

Extensions

Edited and extended by Max Alekseyev, Feb 06 2010

A165290 Numbers which cannot be represented as a cube - nearest square (cube >= square).

Original entry on oeis.org

1, 3, 5, 6, 8, 9, 10, 12, 14, 15, 16, 17, 18, 21, 22, 23, 24, 25, 27, 29, 30, 31, 32, 33, 34, 36, 37, 38, 41, 42, 43, 44, 46, 50, 51, 52, 54, 57, 58, 59, 61, 62, 64, 65, 66, 68, 69, 70, 71, 72, 73, 75, 77, 78, 80, 82, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Sep 13 2009

Keywords

Comments

Complement of A165288.

Crossrefs

Cf. A165288, A165289

Programs

  • Mathematica
    lst={}; Do[a=n^3-Floor[Sqrt[n^3]]^2; If[a<=508,AppendTo[lst,a]],{n,2*8!}]; lst=Take[Union@lst,90]; lst1={}; Do[AppendTo[lst1,n],{n,508}]; lst1; Complement[lst1,lst]
Showing 1-5 of 5 results.

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

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