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parodites sequence

Three representations of the extended series belonging to the PARODITES SEQUENCE.


threeseries.PNG

 

using the polylogarithmic function

usingpolyalgorithmicfunction.PNG

using the floor function/complex argument


usingfloorfunctions.PNG

usingthegamafunction.PNG

 

You can get a Fibonacci like pattern with the convergents, eg. 118/157 is 115/153 plus 3/4, ; 587/781 is 469/624 plus 118/157

fibbonaccifractions.PNG

 

accumulating them, (the first three numbers here are always primes, by altering the value of log3 you can calculate really big primes, not sure why this pattern is there: 

 

calculatingprimesbyconvergentaccumulation.PNG