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.

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A211022 Value on the axis "y" of the center of the n-th circle formed in the structure of A211000.

Original entry on oeis.org

-6, -4, -2, 0, 2, 6, 8, 4, -10, -12, -8, 10, 12, 14, 16, 20, 22, 24, 26, 30, 32, 34, 36, 28, 38, 40, 42, 46, 48, 52, 56, 58, 60, 62, 54, 50, 44, 64, 66, 68, 18, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 102, 106, 104, 100
Offset: 1

Views

Author

Omar E. Pol, Mar 31 2012

Keywords

Comments

The structure of A211000 looks like essentially a column of tangent circles of radius 1. The structure arises from the prime numbers A000040. Values on the axis "x" are equal to 3.

Crossrefs

Cf. A187210, A211000, A211001-A211003, A211010, A211011, A211020, A211021, A211023, A211024.

A355479 a(n) is the number of distinct honeycomb cell walls built after the n-th step of the walk described in A355478.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 20, 20, 20, 20, 21, 22, 23, 24, 24, 25, 26, 27, 28, 29, 30, 31, 31, 31, 31, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 40, 41, 42, 42, 43, 44, 45, 46, 46, 46, 47, 47, 48, 49, 50, 51, 51, 51
Offset: 0

Views

Author

Paolo Xausa, Jul 18 2022

Keywords

Comments

See A355478 for more information, animations, and illustration of selected terms.

Examples

			In the following diagrams the walk is shown at the end of the n-th step, together with the position of the bee (*).
.
n     0      1      8        28               60
a(n)  0      1      8        24               47
                                         __
                                      __/  \*_
      *      __*   __    __          /  \__/  \__
                     \     \__       \__/  \__   \__
                     /     /  \__       \__/  \__/  \__
                     \     \*_   \__       \__/  \__   \__
                     /     /  \     \            /  \     \
                     \     \__/   __/            \__/   __/
                     /     /   __/               /   __/
                     \*    \__/                  \__/
.

Links

Crossrefs

Cf. A174313, A211020, A233399, A355478, A355480, A357434.

Programs

  • Mathematica
    A355479[nmax_]:=Module[{a={0},w={},p1={0, 0},p2,angle=0},Do[w=Union[w,{Sort[{p1,p2=AngleVector[p1,angle+=If[PrimeQ[n],-1,1]Pi/3]}]}];p1=p2;AppendTo[a,Length[w]],{n,nmax}];a];
A355479[100] (* Paolo Xausa, Jan 05 2023 *)

A355480 a(n) is the number of distinct, hexagonal-tiled regions after the n-th step of the walk described in A355478.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Jul 21 2022

Keywords

Comments

See A355478 for additional information and animations.

Examples

			In the following diagrams the walk is shown at the end of the n-th step, together with the position of the bee (*).
.
n     0      1      8        28               60
a(n)  0      0      0         1                2
                                         __
                                      __/ 2\*_
      *      __*   __    __          / 2\__/  \__
                     \     \__       \__/ 2\__   \__
                     /     /  \__       \__/ 2\__/  \__
                     \     \*_   \__       \__/  \__   \__
                     /     / 1\     \            / 1\     \
                     \     \__/   __/            \__/   __/
                     /     /   __/               /   __/
                     \*    \__/                  \__/
.

Links

Crossrefs

Cf. A174313, A211020, A233399, A355478, A355479.

Programs

  • Mathematica
    A355480[nterms_]:=Module[{a={0},walk={{0,0}},angle=0,cells},Do[AppendTo[walk,AngleVector[Last[walk],angle+=If[PrimeQ[n],-1,1]Pi/3]];cells=FindCycle[Graph[MapApply[UndirectedEdge,Partition[walk,2,1]]],{6},All];AppendTo[a,Length[ConnectedComponents[Graph[Flatten[cells]]]]],{n,nterms-1}];Take[a,nterms]];
A355480[100]
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