The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A129757 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A129757

a(n) = ceiling((2^n + 1 - 2*floor(2^(n/2)))/2).
(history; published version)

#16 by Joerg Arndt at Sat Aug 08 01:45:19 EDT 2020

STATUS

proposed

approved

#15 by Joerg Arndt at Fri Aug 07 02:04:12 EDT 2020

STATUS

editing

proposed

#14 by Joerg Arndt at Fri Aug 07 02:03:35 EDT 2020

NAME

a(n) = ceiling(g) where g satisfies (2^n + 1 - 2*floor(2^(n/2)) - 2 + 2*g - ()/2^n - 1) = 0.

MATHEMATICA

Ceiling[Flatten[Table[N[Flatten[g /. Solve[2*Floor[2^(n/2)] - 2 + 2*g - (2^n - 1) == 0, g]]], {n, 1, 32}]]]

KEYWORD

nonn,easy,less,changed

EXTENSIONS

Edited by Michel Marcus and Joerg Arndt, Aug 07 2020

STATUS

proposed

editing

Discussion

Fri Aug 07

02:04

Joerg Arndt: OMG, the levels of obfuscations are endless.  Thanks.

#13 by Michel Marcus at Fri Aug 07 01:54:27 EDT 2020

STATUS

editing

proposed

#12 by Michel Marcus at Fri Aug 07 01:54:23 EDT 2020

PROG

(PARI) a(n) = ceil((2^n + 1 - 2*floor(2^(n/2)))/2); \\ Michel Marcus, Aug 07 2020

STATUS

proposed

editing

#11 by Joerg Arndt at Fri Aug 07 01:29:53 EDT 2020

STATUS

editing

proposed

#10 by Joerg Arndt at Fri Aug 07 01:27:45 EDT 2020

NAME

Maximum genus of fixed edge 2^m-1 binary state graph with 2*m+1 states: Vertices(n)=Floor[2^(n/2)]; Faces(n)=Floor[2^[m-n/2]; Edges(n)=Vertices(n)+Faces(n)-2+2*g=2^m-1; solved for g at the central point m.

a(n) = ceiling(g) where g satisfies 2*floor(2^(n/2)) - 2 + 2*g - (2^n - 1) = 0.

KEYWORD

nonn,uned,less,changed

Discussion

Fri Aug 07

01:29

Joerg Arndt: Removed Bagula's demented blathering. Can someone check?

#9 by Joerg Arndt at Fri Aug 07 01:24:09 EDT 2020

COMMENTS

The idea was to get a binary graph system of vertices, edges and faces that had a genus near the exceptional group sequence dimension. It is a form of combinatorial optimization. The object was to get an idea of what higher dimensional exceptional group dimensions would look like if they existed.

FORMULA

a(n) =Ceiling[Flatten[Table[N[Flatten[g /. Solve[2*Floor[2^(n/2)] - 2 + 2*g - (2^n - 1) == 0, g]]], {n, 1, 32}]]]

EXAMPLE

Exceptional group dimension to output:

14->12->G2

24 ->25->A4

52 ->54->F4

133->113->E7

248->235->E8

484->481->E9

(?)->980->E10

Example 21 state system 2^10:

a = Table[Flatten[{n/20, N[Flatten[g /. Solve[v[n] + f[n] - 2 + 2*g - 1023 == 0, g]]/480.5]}], {n, 0, 20}];

ListPlot[a, PlotJoined -> True]

The normalized to one Plot has the form of dimension for a multifractal system.

STATUS

reviewed

editing

Discussion

Fri Aug 07

01:26

Joerg Arndt: Let me try: 
"a(n) = ceiling(g) where g satisfies 2*floor(2^(n/2)) - 2 + 2*g - (2^n - 1) = 0."

#8 by Hugo Pfoertner at Fri Aug 07 01:03:51 EDT 2020

STATUS

proposed

reviewed

#7 by Michel Marcus at Fri Aug 07 01:00:35 EDT 2020

STATUS

editing

proposed

Discussion

Fri Aug 07

01:03

Hugo Pfoertner: "Reviewed these changes" then really has to taken verbally, nothing beyond.