Wednesday, September 30, 2015

Two Sequences with Interesting Results

9/30/2015



Today I want to put together Sequence number for the 1, -1, 1 Tribonacci Sequence and the 1, 0, -1, 1 Tetranacci Sequence.  They produce some intriguing results.

The 1, -1, 1 Tribonacci Sequence: a(0) = a(1) = 1, a(2) = 1, and when n>2 then a(n) = a(n-1) – a(n-2) + a(n-3).
The Sequence Number is: 909
(I can use a shorter Sequence Number because all I need for this sequence is single digit strings.)
1/909 =
0.
0  0  1  1  0  0  1  1  0  0  1  1  0  0  1  1  0  0  1  1  0  0  1  1 
This is a repeating decimal with a period of four.
All term are accurate up to infinity.
Compare with OEIS sequence A021913.

The 1, 0, -1, 1 Tetranacci Sequence: a(0) = a(1) = a(2) = 0, a(3) = 1, and when n>3 then a(n) = a(n-1) – a(n-3) + a(n-4).
The Sequence Number is: 9009
1/9009 =
0.
0  0  0  1  1  1  0  0  0  1  1  1  0  0  0  1  1  1  0  0  0  1  1  1 
This is a repeating decimal with a period of 6.
All terms are accurate up to infinity!
This sequence is not listed in the OEIS – yet.


David

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