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.

A070127 Numbers n such that [A070080(n), A070081(n), A070082(n)] is an obtuse integer triangle.

Original entry on oeis.org

5, 8, 13, 14, 20, 21, 25, 26, 29, 30, 32, 36, 37, 41, 42, 44, 49, 50, 52, 56, 57, 59, 61, 62, 66, 67, 69, 74, 75, 77, 78, 79, 80, 82, 86, 87, 89, 91, 96, 97, 99, 100, 101, 102, 104, 105, 110, 111, 113, 115, 118, 122, 123, 125, 126, 127
Offset: 1

Views

Author

Reinhard Zumkeller, May 05 2002

Keywords

Examples

			a(10)=30: [A070080(30), A070081(30), A070082(30)]=[3,5,7], A070085(30)=3^2+5^2-7^2=9+25-49=-15<0.

Links

Crossrefs

Cf. A070101, A070129, A070130, A070131, A070132, A070133, A070134, A070135, A070128, A070085.

Programs

  • Mathematica
    m = 55 (* max perimeter *);
sides[per_] := Select[Reverse /@ IntegerPartitions[per, {3}, Range[ Ceiling[per/2]]], #[[1]] < per/2 && #[[2]] < per/2 && #[[3]] < per/2 &];
triangles = DeleteCases[Table[sides[per], {per, 3, m}], {}] // Flatten[#, 1]& // SortBy[Total[#] m^3 + #[[1]] m^2 + #[[2]] m + #[[1]]&];
Position[triangles, {a_, b_, c_} /; a^2 + b^2 - c^2 < 0] // Flatten (* Jean-François Alcover, Oct 11 2021 *)

A070115 Numbers m such that [A070080(m), A070081(m), A070082(m)] is an isosceles integer triangle.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 14, 15, 16, 18, 19, 22, 23, 24, 26, 27, 28, 31, 32, 34, 35, 38, 39, 40, 43, 46, 47, 48, 51, 52, 54, 55, 58, 61, 63, 64, 65, 68, 71, 72, 73, 76, 81, 82, 84, 85, 88, 91, 93, 94, 95, 98, 103, 104, 107, 108
Offset: 1

Views

Author

Reinhard Zumkeller, May 05 2002

Keywords

Examples

			26 is a term because [A070080(26), A070081(26), A070082(26)] = [4=4<6].

Links

Crossrefs

Cf. A059169, A070116, A070117, A070124, A070125, A070126, A070133, A070134, A070135.

Programs

  • Mathematica
    m = 55 (* max perimeter *);
sides[per_] := Select[Reverse /@ IntegerPartitions[per, {3}, Range[ Ceiling[per/2]]], #[[1]] < per/2 && #[[2]] < per/2 && #[[3]] < per/2 &];
triangles = DeleteCases[Table[sides[per], {per, 3, m}], {}] // Flatten[#, 1]& // SortBy[Total[#] m^3 + #[[1]] m^2 + #[[2]] m + #[[1]] &];
Position[triangles, {a_, a_, b_} | {a_, b_, b_}] // Flatten (* Jean-François Alcover, Oct 12 2021 *)

A070106 Number of integer triangles with perimeter n which are obtuse and isosceles.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 4, 4, 3, 3, 4, 4, 3, 4, 4
Offset: 1

Views

Author

Reinhard Zumkeller, May 05 2002

Keywords

Comments

a(n)=A070101(n)-A024156(n); a(n)=A059169(n)-A070098(n).

Examples

			For n=11 there are A005044(11)=4 integer triangles: [1,5,5], [2,4,5], [3,3,5] and [3,4,4]; only one of the two obtuses ([2,4,5] and [3,3,5]) is also isosceles; therefore a(11)=1.

Links

Crossrefs

Cf. A070080, A070081, A070082, A059169, A070107, A070108, A070133.
Showing 1-3 of 3 results.

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

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