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.

A371071 Squared volumes of tetrahedra with integer edge lengths, multiplied by 144.

Original entry on oeis.org

2, 11, 14, 26, 34, 44, 47, 54, 59, 62, 74, 98
Offset: 1

Views

Author

Hugo Pfoertner, Mar 18 2024

Keywords

Comments

The larger terms depend on a lower bound for the minimum volume, which is not yet available. Therefore the data > 100 was removed. See A371072 for progress in determining this lower bound.

Links

Crossrefs

Cf. A097125, A208454, A371070, A371072, A371344.

A371344 a(n)/144 is the minimum squared volume > 0 of a tetrahedron with integer edge lengths whose largest is n.

Original entry on oeis.org

2, 11, 26, 47, 54, 107, 146, 191, 242, 299, 191, 134, 146, 146, 151, 767, 423, 151, 854, 558, 764, 491, 503, 464, 146, 146, 431, 944, 666, 146, 146, 350, 599, 311, 599, 511, 1719, 2286, 944, 1871, 1679, 990, 2714, 1907, 990, 551, 959, 1199, 1244, 990, 1206, 854, 764
Offset: 1

Views

Author

Hugo Pfoertner, Mar 19 2024

Keywords

Examples

			a(1) = 2 corresponds to the regular tetrahedron with all edges equal to 1. Its volume is sqrt(2/144) = 0.11785113...

Links

Crossrefs

Cf. A097125, A371072, A371345.
Subset of A371071.
A001014(n)/72 are the corresponding maximum squared volumes.

Programs

  • PARI
    \\ See A371345. Replace final #Set(Vec(L)) by vecmin(Vec(L))/2
\\ Second version using simple minded loops and triangle inequalities
\\ Not suitable for larger n
a371344(n) = {my (Vmin=oo,w=vector(6)); w[1]=n; for(w2=1,n,w[2]=w2; for(w3=1,n,w[3]=w3; for(w4=1,n,w[4]=w4; for(w5=1,n,w[5]=w5; for(w6=1,n,w[6]=w6;
forperm (w, v, if(v[4]+v[5]0, Vmin=min(Vmin,CM)))))))); Vmin/2}; \\ return value corrected by M. F. Hasler, Dec 02 2024
  • PARI
    /* equivalent to the preceding, but simplified */
A371344(n) = {my (Vmin=oo,CM, n2=n^2); forvec(v=vector(5,k,[1,n]), v[4]+v[5]= Vmin || Vmin=CM); Vmin/2} \\ M. F. Hasler, Dec 02 2024

Extensions

a(33), a(37), a(38), and a(43) corrected by Hugo Pfoertner, Dec 03 2024

A371073 a(n)/144 is the maximum squared volume of a tetrahedron with the sum of its integer edge lengths equal to n.

Original entry on oeis.org

11, 14, 44, 128, 108, 188, 368, 448, 828, 1458, 1584, 2151, 3159, 3824, 5616, 8192, 9200, 11504, 15104, 17975, 23600, 31250, 35100, 41975, 51875, 60444, 74700, 93312, 104076, 120924, 143856, 164591, 195804, 235298, 260288, 296303, 343343, 387008, 448448, 524288
Offset: 9

Views

Author

Hugo Pfoertner, Mar 19 2024

Keywords

Examples

			a(12) = 128 corresponds to the regular tetrahedron with all edges equal to 2. Its volume is V=sqrt(2)*2^3/12; V^2 = 2*2^6/12^2 = 128/144.

Crossrefs

Cf. A097125, A208454, A371070, A371072.
Subset of A371071.
Showing 1-3 of 3 results.

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