The Amalgamation Formulae and Iterations of Mono-digit Pedigree

Author(s)	HUMPHREY TAKUNDA MUCHAPIREYI
Country	Zimbabwe
Abstract	In this paper we present equations to generate the concatenation of natural numbers A∈N. The main ingredient of our study is the innocuous repunit of a number R_A ; and in this study we introduce three amalgamation operators: ↕ for the constant, ↑ for the incremental and ↓ for the detrimental cases of concatenation according to a variable arithmetic progression. Our method of amalgamation demonstrates the generation of common number sequences, as well as how any two different natural numbers can be joined and alternated, depending on which of the numbers should be displayed first. We also introduce an operator Ω(A ) based on repunits and whose dynamics yields two constants H_(o )and H_(e )which we calculate. Amongst the few corollaries from this conjecture is an identity stating that the product of the repunits of those irrational numbers R_(H_o ) R_(H_e )is equal to unity.
Keywords	concatenation , repunit, amalgamation, sequences
Field	Mathematics
Published In	Volume 5, Issue 6, November-December 2023
Published On	2023-12-11
Cite This	The Amalgamation Formulae and Iterations of Mono-digit Pedigree - HUMPHREY TAKUNDA MUCHAPIREYI - IJFMR Volume 5, Issue 6, November-December 2023. DOI 10.36948/ijfmr.2023.v05i06.10239
DOI	https://doi.org/10.36948/ijfmr.2023.v05i06.10239
Short DOI	https://doi.org/gs84b8

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