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.

A022561 Numbers that are not the sum of 3 nonnegative cubes.

Original entry on oeis.org

4, 5, 6, 7, 11, 12, 13, 14, 15, 18, 19, 20, 21, 22, 23, 25, 26, 30, 31, 32, 33, 34, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 56, 57, 58, 59, 60, 61, 63, 67, 68, 69, 70, 71, 74, 75, 76, 77, 78, 79, 82, 83, 84, 85, 86, 87, 88, 89
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Complement of A004825.

Programs

A185345 Numbers that are not the sum of two rational cubes.

Original entry on oeis.org

3, 4, 5, 10, 11, 14, 18, 21, 23, 24, 25, 29, 32, 36, 38, 39, 40, 41, 44, 45, 46, 47, 52, 55, 57, 59, 60, 66, 73, 74, 76, 77, 80, 81, 82, 83, 88, 93, 95, 99, 100, 101, 102, 108, 109, 111, 112, 113, 116, 118, 119, 121, 122, 129, 131, 135, 137, 138, 144, 145, 146, 147
Offset: 1

Views

Author

Arkadiusz Wesolowski, Mar 17 2012

Keywords

Examples

			22 can be expressed as (17299/9954)^3 + (25469/9954)^3, so 22 is not in the sequence.

References

  • Henri Cohen, Number Theory - Volume I: Tools and Diophantine Equations, Springer-Verlag, 2007, pp. 378-379.
  • Yu. I. Manin, A. A. Panchishkin, Introduction to Modern Number Theory: Fundamental Problems, Ideas and Theories (Second Edition), Springer-Verlag, 2006, pp. 43-46.

Links

Crossrefs

Complement of A159843. One subsequence of this sequence is A022555, numbers that are not the sum of two nonnegative integer cubes.

Programs

  • Magma
    lst1:=[]; lst2:=[x^3+y^3: x, y in [0..5]]; for n in [1..147] do if IsZero(Rank(EllipticCurve([0, 16*n^2]))) and not n in lst2 then lst1:=Append(lst1, n); end if; end for; lst1;
  • Mathematica
    (* A naive program with a few pre-computed terms from A159843 *) nmax = 122; xmax = 3000; CubeFreePart[n_] := Times @@ Power @@@ ({#[[1]], Mod[#[[2]], 3]}& /@ FactorInteger[n]); nn = Join[{1}, Reap[Do[n = CubeFreePart[x*y*(x+y)]; If[1 < n <= nmax, Sow[n]], {x, 1, xmax}, {y, x, xmax}]][[2, 1]] // Union]; A159843 = Select[ Union[nn, nn*2^3, nn*3^3, nn*4^3, {17, 31, 53, 67, 71, 89, 94, 103, 107, 122}], # <= nmax &]; Complement[Range[nmax], A159843] (* Jean-François Alcover, Feb 10 2015 *)
  • PARI
    isok(k) = my(v=thue('x^3+1, k)); if(!(#v>0 && #select(k->k>=0, concat(v))>#v) && ellanalyticrank(ellinit([0, 16*k^2]))[1]==0, 1, 0); \\ Arkadiusz Wesolowski, May 21 2023

A292740 Indices k such that A292547(k) = 0.

Original entry on oeis.org

2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70
Offset: 1

Views

Author

Vaclav Kotesovec, Sep 22 2017

Keywords

Comments

Complement of A290276.
Conjecture: for k > 212594 there are no more terms in this sequence (tested for k < 63000000).

Examples

			3 is in the sequence because A292547(3) = 0
8 is not in the sequence because A292547(8) = -1
201254 is in the sequence because A292547(201254) = 0
212594 is in the sequence because A292547(212594) = 0

Links

Crossrefs

Cf. A276517, A279329, A279486, A279529, A290276, A292547.
Cf. A001476, A022555, A031980.

Programs

  • Mathematica
    With[{nn = 200}, -1 + Position[#, 0][[All, 1]] &@ CoefficientList[ Series[Product[1 + x^((2 k - 1)^3), {k, 1, Floor[nn^(1/3)/2] + 1}], {x, 0, nn}], x]] (* Michael De Vlieger, Sep 22 2017, after Vaclav Kotesovec at A292547 *)

A057903 Positive integers that are not the sum of exactly two positive cubes.

Original entry on oeis.org

1, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79
Offset: 1

Views

Author

Eric W. Weisstein

Keywords

Comments

Includes the cubes themselves (since a^3 = b^3 + c^3 has no solution, by the exponent 3 case of Fermat's Last Theorem), so is different from A022555.

Links

Crossrefs

Cf. A022555, A000578.

Programs

  • Mathematica
    pr[n_] := Select[ PowersRepresentations[n, 2, 3], FreeQ[#, 0]& ]; Select[ Range[80], pr[#] == {} &] (* Jean-François Alcover, Nov 08 2012 *)

Formula

Equals A022555 union A000578 - {0}.

Extensions

Edited by N. J. A. Sloane, Sep 28 2007

A139211 Partial sums of A003325.

Original entry on oeis.org

2, 11, 27, 55, 90, 144, 209, 281, 372, 498, 626, 759, 911, 1100, 1317, 1541, 1784, 2034, 2314, 2655, 2999, 3350, 3720, 4127, 4559, 5027, 5540, 6060, 6599, 7158, 7734, 8371, 9057, 9785, 10515, 11252, 12008, 12801, 13655, 14510, 15455, 16456, 17464, 18488
Offset: 1

Views

Author

Jonathan Vos Post, Jun 06 2008

Keywords

Examples

			a(15) = 2 + 9 + 16 + 28 + 35 + 54 + 65 + 72 + 91 + 126 + 128 + 133 + 152 + 189 + 217 = 1317.

Crossrefs

Cf. A000578, A003325, A022555, A057903.

Programs

  • Mathematica
    Accumulate[With[{upto=2000},Select[Total/@Tuples[Range[Ceiling[Surd[ upto,3]]]^3,2],#<=upto&]]//Union] (* Harvey P. Dale, Apr 27 2022 *)

Extensions

a(29)-a(44) from Nathaniel Johnston, Sep 26 2011
Showing 1-5 of 5 results.

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

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