Friday, 25 January 2019

sequences and series - How to replace addition with multiplication to find the next integer value?



Sorry in advance for my lack of mathematical knowledge, I am very new to it.






Yesterday, I posed this question to myself:




"In a world without addition or subtraction, how could we derive the next value in the sequence of natural numbers from 1 with a step size of 1?"



This lead me to the idea of multiplication to find the next value in a sequence. After analyzing the multipliers between each natural value using:
(n+1)n



I noticed the pattern of this sequence starts at the high values of 2 and 1.5, then converges to a value of 1.







My two questions:




  • Is it right to assume that the sequence of multipliers should have a more predictable sequence?

  • Are there more elegant ways of producing the next natural number without addition or subtraction?


Answer



With the function 2n and it's inverse, log2 available,
n+1=log2(22n).



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