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 1-3 of 3 results.

A351375 Least nonnegative integer m such that n = x^5 + y^5 - (z^3 + m^3) for some nonnegative integers x,y,z with z <= m.

Original entry on oeis.org

0, 0, 0, 174, 3, 3, 3, 53, 53, 25, 3, 20, 93, 932, 1132, 405, 2, 2, 7, 6, 6, 972, 39712, 2, 2, 2, 6, 6, 6, 3, 1, 1, 0, 0, 271, 43, 3, 3, 14, 14, 42, 583, 131, 181, 1131, 15, 93, 176, 2, 48, 685, 6, 16, 16, 5, 2, 2, 559, 6, 6, 1351, 421, 1, 1, 0, 60, 12, 12, 300, 29, 14, 20, 53, 52
Offset: 0

Views

Author

Zhi-Wei Sun, Feb 09 2022

Keywords

Comments

Conjecture: a(n) exists for any nonnegative integer n.
See also Conjecture 1 in A351341.

Examples

			a(3) = 174 with 3 = 11^5 + 22^5 - 36^3 - 174^3.
a(13) = 932 with 13 = 12^5 + 61^5 - 328^3 - 932^3.
a(14) = 1132 with 14 = 40^5 + 67^5 - 125^3 - 1132^3.
a(15) = 405 with 15 = 31^5 + 36^5 - 283^3 - 405^3.
a(21) = 972 with 21 = 37^5 + 64^5 - 608^3 - 972^3.
From _Chai Wah Wu_, Feb 21 2022: (Start)
a(22) = 39712 with 22 = 106^5 + 599^5 - 24385^3 - 39712^3.
a(154) = 22049 with 154 = 163^5 + 432^5 - 16438^3 - 22049^3.
a(246) = 22811 with 246 = 161^5 + 412^5 - 4786^3 - 22811^3.
a(446) = 230630 with 446 = 843^5 + 1771^5 - 177372^3 - 230630^3.
a(769) = 614692 with 769 = 2320^5 + 2777^5 - 46750^3 - 614692^3.
(End)

Links

Crossrefs

Cf. A000578, A000584, A004842, A004999, A351338, A351341, A351376.

Programs

  • Mathematica
    FQ[n_]:=IntegerQ[n^(1/5)];
tab={};Do[m=0;Label[bb]; k=m^3;Do[If[FQ[n+k+x^3-y^5], tab=Append[tab,m];Goto[aa]],{x,0,m},{y,0,((n+k+x^3)/2)^(1/5)}];m=m+1;Goto[bb];Label[aa],{n,0,21}];Print[tab]

Extensions

a(22)-a(73) from Chai Wah Wu, Feb 21 2022

A351376 Least nonnegative integer m such that n = x^3 + y^3 - (z^5 + m^5) for some nonnegative integers x,y,z with z <= m.

Original entry on oeis.org

0, 0, 0, 2, 76, 3, 1, 1, 0, 0, 6, 5, 4, 7, 1, 1, 0, 51, 129, 14, 22, 2, 2, 4, 136, 1, 1, 0, 0, 27, 7, 2, 2, 1, 1, 0, 3, 3, 14, 2, 2, 44, 11, 5, 8, 6, 101, 4, 4, 28, 14, 6, 1, 1, 0, 17, 42, 33, 2, 2, 20, 2, 1, 1, 0, 0, 3, 8, 3, 2, 1, 1, 0, 3, 6, 41, 3, 43, 12, 10, 10, 6, 6, 6, 59, 29, 33, 81, 2, 1, 1, 0, 2, 2, 2, 2, 2, 3, 3, 3, 2
Offset: 0

Views

Author

Zhi-Wei Sun, Feb 09 2022

Keywords

Comments

Conjecture: a(n) exists for any nonnegative integer n.
See also Conjecture 1 in A351341.

Examples

			a(4) = 76 with 4 = 775^3 + 1397^3 - (58^5 + 76^5).
a(18) = 129 with 18 = 1693^3 + 3137^3 - (3^5 + 129^5).
a(24) = 136 with 24 = 2534^3 + 3116^3 - (0^5 + 136^5).
a(87) = 81 with 87 = 140^3 + 1658^3 - (64^5 + 81^5).
From _Chai Wah Wu_, Feb 21 2022 : (Start)
a(389) = 3883 with 389 = 590621^3 + 877987^3 - (612^5 + 3883^5).
a(4173) = 3978 with 4173 = 16112^3 + 1108958^3 - (3259^5 + 3978^5).
(End)

Links

Crossrefs

Cf. A000578, A000584, A004842, A004999, A351338, A351341, A351375.

Programs

  • Mathematica
    CQ[n_]:=IntegerQ[n^(1/3)];
tab={};Do[m=0;Label[bb]; k=m^5;Do[If[CQ[n+k+x^5-y^3], tab=Append[tab,m];Goto[aa]],{x,0,m},{y,0,((n+k+x^5)/2)^(1/3)}];m=m+1;Goto[bb];Label[aa],{n,0,100}];Print[tab]

A351832 Least nonnegative integer m such that n = x^6 + y^6 - (z^2 + m^2) for some nonnegative integers x,y,z with z <= m.

Original entry on oeis.org

0, 0, 0, 6, 6, 20, 7, 7, 19, 24, 24, 7, 6, 6, 5, 5, 7, 26, 26, 6, 6, 22, 9, 5, 5, 6, 98, 6, 6, 6, 5, 5, 4, 4, 32, 5, 5, 26, 5, 4, 4, 20, 322, 7, 4, 4, 3, 3, 4, 4, 22, 3, 3, 22, 3, 3, 2, 2, 418, 2, 2, 2, 1, 1, 0, 0, 94, 6, 23, 20, 7, 19, 24, 20, 20, 7, 6, 22, 5, 7, 19, 18, 18, 6, 22, 37, 59, 5, 6, 24, 24, 6, 6, 21
Offset: 0

Views

Author

Zhi-Wei Sun, Feb 21 2022

Keywords

Comments

Conjecture: a(n) exists for each nonnegative integer n.
See also Conjecture 2 in A351341.

Examples

			a(170) = 2730 with 170 = 9^6 + 15^6 - (2114^2 + 2730^2).
a(5938) = 16184 with 5938 = 17^6 + 25^6 - (2520^2 + 16184^2).
a(9746) = 7600 with 9746 = 11^6 + 21^6 - (5456^2 + 7600^2).

Links

Crossrefs

Cf. A000290, A001014, A001481, A351321, A351338, A351341, A351375, A351376.

Programs

  • Mathematica
    QQ[n_]:=IntegerQ[n^(1/6)];
tab={};Do[m=0; Label[bb]; k=m^2; Do[If[QQ[n+k+x^2-y^6], tab=Append[tab,m];Goto[aa]],  {x, 0, m}, {y, 0, ((n+k+x^2)/2)^(1/6)}];m=m+1; Goto[bb]; Label[aa], {n, 0, 100}];Print[tab]
Showing 1-3 of 3 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.