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Repdigits as sums of three Padovan numbers
1Institute of Analysis and Number Theory, Graz University of Technology, Kopernikusgasse 24/II, 8010 Graz, Austria.
Boletin De La Sociedad Matematica Mexicana
|June 20, 2020
Summary
This study identifies all repdigits, numbers with repeating digits, that are sums of three Padovan numbers. The findings contribute to understanding number sequences and their additive properties.
Area of Science:
- Number Theory
- Sequence Analysis
Background:
- The Padovan sequence is a fascinating integer sequence defined by a recurrence relation.
- Repdigits are numbers consisting of repeating digits in a given base.
- Investigating sums of sequence terms provides insights into number properties.
Purpose of the Study:
- To determine all repdigits in base 10 that can be expressed as the sum of three Padovan numbers.
- To explore the intersection of Padovan numbers and repdigits.
Main Methods:
- Definition of the Padovan sequence: P(n) = P(n-2) + P(n-3) with initial values.
- Systematic search and analysis of sums of three consecutive or non-consecutive Padovan numbers.
- Verification of sums against the definition of repdigits in base 10.
Main Results:
- Identification of specific repdigits that satisfy the condition.
- Exclusion of other repdigits based on computational or theoretical analysis.
- The set of repdigits that are sums of three Padovan numbers has been fully characterized.
Conclusions:
- The paper provides a complete list of repdigits representable as the sum of three Padovan numbers.
- This research adds to the literature on additive properties of integer sequences.
- The findings may stimulate further research into sums of Padovan numbers and other integer sequences.
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