TESLA MULTIPLICATION SPIRAL, TESLA-ZOLLNER DIGITAL ROOT SEQUENCE, AND THEIR RELATION TO PRIMES AND COMPOSITES

Abstract

In this work we seek to establish, through a formal demonstration, that the digital root of a natural number n, in decimal base, is given by the remainder of the division of n by 9, except in the case where 9|n whose digital root is 9. From this we can deduce that the digital root of a number k is between the numbers 1 and 9, with this the present investigation allows to demonstrate the Transpositioning based
on the Tesla Spiral Multiplication Map (MEMT), published in 1912 and in the digital publication “Nikola Tesla, knows his Multiplication Map”, together with the optimization of the Digital Root Sequences (6k ±1), shows a relative order within the study of prime numbers, managing to define the Real Strip of Prime Numbers (FRNP) within the universe of natural integers. In this way, a sequential pattern can be considered to determine the factors that make up a composite number, beingable to represent and establish the Tesla Zollner Digital Root Sequence (STZRd) namely (741 − 528 − 396).