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I think I have found the rule that explains, not exactly doubling, but increment patterns of the decimal sequences. It just needs elaboration and tuning.
For reciprocal primes below 10, for example 1/7 substract 7 from 10 and use it as an increment base:
Sum[(10-7)^(n-1)/10^n, {n, 1, Infinity}] = Sum[3^(n-1)/10^n, {n, 1, Infinity}]
=> 0.142857...
Or the beginning of the iteration:…
ContinuePosted on July 20, 2015 at 9:00am
1/7 has a repeating pattern as we know: .142857
This can be seen also as a doubling of 7 with two decimal slot addition:
07.14 28 56 112 224 448 896 ->…
ContinuePosted on January 28, 2015 at 9:30am
I just realized, why all modulos has a repeating patterns in Fibonacci sequence. It is because every prime number has a repeating cycle on the sequence. 72 first Fibonacci numbers has 63 prime divisors and they appear in certain index of the Fibonacci sequence.
{0: 1, -> number 1 is a divisor for all numbers
2: 3, -> number 2 repeats every third position
3: 4, -> number 3 repeats every fourth position. thus number 6 will repeat every 12 position
5:…
Posted on November 26, 2014 at 12:30pm — 3 Comments
Reducing fibonacci sequence by mirroring its digital root 9 pattern:
1 1 2 3 5 8 4 3 7 1 8 9
8 8 7 6 4 1 5 6 2 8 1 9
- - - - - - - - - - - -
9 9 9 9 9 9 9 9 9 9 9 9
Vertical grouping:
1 8 9 A
1 8 9 A
2 7 9 B
3 6 9 C
5 4 9 D
8 1 9 A-
4 5 9 D-
3 6 9 C
7 2 9 B-
1 8 9 A
8 1 9 A-
9 9 …
Posted on November 18, 2014 at 11:30am
glad to have you here, let's start some threads!!!
it's difficult to say with certainty what the 'open questions' are ... I think it's different for everyone. What are YOU'RE questions???
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