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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.

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A222624 Sequence of dimensions of a regular simplex with unit edge that has at least one inter-hypersphere with a rational radius (including the radii of the in-hypersphere and circum-hypersphere).

Original entry on oeis.org

1, 7, 8, 17, 23, 31, 35, 49, 55, 62, 71, 74, 80, 89, 95, 97, 119, 120, 127, 143, 146, 161, 174, 199, 215, 223, 224, 241, 244, 251, 287, 288, 293, 299, 305, 323, 337, 359, 360, 362, 383, 391, 424, 440, 449, 479, 483, 489, 503, 511, 566, 574, 575, 577, 587, 599
Offset: 1

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Author

Frank M Jackson, Feb 26 2013

Keywords

Comments

The radius of the inter-hypersphere of a regular simplex of dimension k with unit edge is given by r=Sqrt((k-j)/(2*(k+1)*(j+1))) where 0<=j

Examples

			a(3)=8 because it is the 3rd value of k with k=8 that has an inter-hypersphere of rational radius. In fact in dimension 8 the regular simplex with unit edge has 4 inter-hyperspheres of rational radius. They are 2/3 at j=0 (circum-hypersphere), 1/3 at j=2, 1/6 at j=5 and 1/12 at j=7 (in-hypersphere).

Links

Crossrefs

Cf. A155946.

Programs

  • Mathematica
    maxlen = 100; getlist[n_] := (d = 0; sublist = {}; While[d < n, If[IntegerQ[Numerator[Sqrt[(n-d)/(2(n+1)(d+1))]]*Denominator[Sqrt[(n-d)/(2(n+1)(d+1))]]], (sublist=Append[sublist, d]; d++), d++]]; sublist);                                           m = 1; fulllist = {}; While[Length[fulllist] <= maxlen, If[Length[getlist[m]]==0, m++, (fulllist=Append[fulllist, m]; m++)];]; fulllist

Formula

a(n)=k is the n-th occurrence for which k=sqrt((k-j)/(2*(k+1)*(j+1))) is rational for at least one value of j in the range 0<=j
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