Comment to Anthony Morris work @ http://www.newunderstandings.com/composite-numbers-analysis/

Where there was no congruence before, there is now. A 12 digit repeating sequence – 12 notes of the Octave?…..2 3 4 6 8 0 1 3 5 6 7 0

This can be broken down into 3 x 4 segments to illustrate the Family Number Groups in the columns created.2 3 4 68 0 1 35 6 7 0

The following is what I saw when I analyzed the mod9 sequence you presented in the same manner learned from Vedic Square unravellings.I don’t believe I can say anything towards what I think it means outside of the pleasant outcomes that are found with mod9 analysis. But provide additional

levels of unravelling… with a smile So the MOD9 sequence on the left, presented with data to the right:

n 1 2 3 4 5 6 7 8 9 10 11 12x 2 3 4 6 8 9 1 3 5 6 7 9

SUM MOD9 COUNT MOD963 9 12 3

Additional data now as we have the extra level of digits to apply operations / functions across – xa + xb – the two halves together.

n 1 2 3 4 5 6

xa 2 3 4 6 8 9xb 1 3 5 6 7 9n 7 8 9 10 11 12

SUM MOD9 COUNT MOD9

32 5 6 631 4 6 6

SUM 3 6 9 12 15 18MOD9 3 6 9 3 6 9

DIFF +3

369 -> the +3 sequence. MOD9 sequence as a result of adding both halves together.

54 = MOD9 sums of first and second row (5)(4)

NUMBER 1 2 3 4 5 6 7 8 9COUNT 1 1 2 1 1 2 1 1 2

Next, splitting the sequence in exact same manner as presented with 4x3 grid above.

Split in half – to 2x6 grid with data on the right…

n 1 2 3 4 5 6

xa 2 3 4 6 8 9Xc 9 7 6 5 3 1n 12 11 10 9 8 7

SUM 11 10 10 11 11 10

MOD9 2 1 1 2 2 1

DIFF +8+9+1+9

Flip of bottom row – going from a straight line sequence, to a double level grid was looked at previously as a shift of last half of sequence under the first half (referred to later as Cross Fold). This to the left, is looking at the sequence as a loop half (referred to later as Loop Fold) – leading us to adding the numbers to a circle and linking numbers according to equilibral geometry.

The numbers indicated in the DIFF field of the table (+8+9+1+9) leads to a whole additional sequence investigation

Equilateral triangles placed in the circle of digits (a vertex each second digit – resulting in 2 triangles, equilateral, (3 angles of 60 = 180 369 The numbers linked in blue = 1 4 7 And linked in green = 2 5 8

3 6 9 I see presentable in a couple of ways… like axis here:

Or as additional triangles:

NB: Same actions taken with the Fibonacci Sequence in MOD9 produce this direction of results too.

Linking up the doubling sequence.:

The numbers indicated in the diff value (+8+9+1+9) when manipulated in MOD9 can output some interesting data too.

In MOD9 I see that to get from 8 to 9 we +1, from 9 to 1 we +1, from 1 to 9 +8…Each difference is analysed for the next level of sequence.

After 24 iterations, we can spot symmetry in the output in a couple of further levels… it just goes on and on

Do all sequence analysis levels give such outputs, or is there something specific about the original 211221 ?

Well, when we check what the difference/interval is between sequential digits in the initial sequence in MOD9 – something similar is occurring.

+9+1+9+8 – that’s the 19th iteration of the interval analysed just before… meaning this will also loop after 24 iterations.

NB: Count of each digit occurrence from slide 1 has similarities wouldn’t you say? 1 1 2

Horizontal sums again producing 54.Vertical sums showing 2 variants. 639 (where 369 was the first Cross Fold result) and 432 which has to be a coinci…ah! wait… no, sorry… gotcha ;) 432 makes a second appearance soon too..

Splitting in half again won’t happen… but we have got the original layered result from the paper which we could table up from. 639 & 693

Back to the splitting of the initial sequence by half – from 12x1 -> 6x2 -> 3x4

SUM MOD9 SUM MOD9 SUM MOD9 SUM MOD9

2 3 4 9 9 2 3 4 9 9 2 3 4 9 9 2 3 4 9 9

6 8 9 23 5 1 3 5 9 9 9 7 6 22 4 6 8 9 23 5

1 3 5 9 9 6 8 9 23 5 6 8 9 23 5 9 7 6 22 4

6 7 9 22 4 6 7 9 22 4 5 3 1 9 9 5 3 1 9 9

CROSS FOLD LOOP FOLD

SUM 15 21 27 SUM 15 21 27 SUM 22 21 20 SUM 22 21 20

MOD9 6 3 9 MOD9 6 3 9 MOD9 4 3 2 MOD9 4 3 2

SUM MOD9

2 3 4 6 15 68 9 1 3 21 35 6 7 9 27 9

SUM 15 18 12 18MOD9 6 9 3 9

The MOD9 output may contain a palindromic number… 2596556952 – the 99 could just as easily be added either end, the balance and essence is still a potential.

Back to sequence analysis… this time outputting to the operation of cumulative sum – as well as in MOD9… both rows of produce some interesting data. Sum’s too.

2 3 4 6 8 9 1 3 5 6 7 9 SUM MOD9

CUM. 2 5 9 15 23 32 33 36 41 47 54 63 360 9

MOD9 2 5 9 6 5 5 6 9 5 2 9 9 72 9

With other cumulative sum sequences I have analyzed, I would repeat the cumulative sum on the MOD9 result a few more times It takes up quite some space to display the data but the results table is below.

The MOD9 output may contain a palindromic number… 2596556952 – the 99 could just as easily be added either end, the balance and essence is still a potential.

Back to sequence analysis… this time outputting to the operation of cumulative sum – as well as in MOD9… both rows of produce some interesting data. Sum’s too.

2 3 4 6 8 9 1 3 5 6 7 9 SUM MOD9

CUM. 2 5 9 15 23 32 33 36 41 47 54 63 360 9

MOD9 2 5 9 6 5 5 6 9 5 2 9 9 72 9

Again some interesting sum’s… but additionally 2 new 6 digit numbers to continue the fractal analysis down another level or two…

Nevertheless, we have a new sequence of numbers to analyse. And like with the DIFF analysis – we could go deeper… back to the initial sequence analysis for now. Staggering the digits as follows:

Those 2x 6 digit numbers… seem nicely balanced… look at how the 147 is evenly spaced by 258 (vice versa too) for each of those numbers.

I wonder where the version for MOD9 = 6? Well, we could replicate would it could look like, couldn’t we?

Also spotted that adding the 1st digit to 6th, 2nd to the 5th and the 3rd to the 4th – we get these results:

Again another route of investigation pops up… so just before we head back to the staggered arrangement analysis, a quick look at these 3x 6 digit numbers.

275184518427751842

These are permutations right? So we could place one of these into a circle to analyse.

Linking up the doubling sequence.:

Similar as the last circle analysis:The numbers linked in blue = 1 4 7 And linked in green = 2 5 8

Out from circles, back to lines. Here marking with the use of arcs in Geogebra the doubling sequence and then making a version with completed circles.

Might be worth to do this for the initial sequence too.

A bit further back, to the staggered arrangement analysis, just to end off that element before closing up with these last few upcoming branches of analysis. Operation of addition in a couple of manners, outputs noted as additional sequences… of specific numbers

Might be worth to do this for the initial sequence too.

TO DO – also the reverse versions perhaps?

Blabla blabalblalba

n 1 2 3 4 5 6

xa 2 3 4 6 8 9xb 1 3 5 6 7 9n 7 8 9 10 11 12

TO DO - Out from circles, back to lines. Here marking with the use of arcs in Geogebra the doubling sequence and then making a version with completed circles.

Might be worth to do this for the initial sequence too.

TO DO - STEP ANALYSIS – doubling sequence TO COMPLETE

Might be worth to do this for the initial sequence too.

TO DO - STEP ANALYSIS TO COMPLETE – SEQUENTIAL & FIBONACCI SEQUENCE

Might be worth to do this for the initial sequence too.