Published July 12, 2025
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Narayana's cows numbers which are concatenations of three repdigits in base ρ

Creators

  • 1. Département de Mathématiques, Faculté des Sciences et Techniques FST, Université de Kara, B.P. 404, Kara, Togo
  • 2. International Chair in Mathematical Physics, and Applications ICMPA-UNESCO Chair, University of Abomey-Calavi, 072 BP. 50, Cotonou, Benin Republic
  • 3. Laboratoire d'Algèbre, de Cryptologie, de Géométrie Algébrique et Applications LACGAA, Departement de Mathematiques et Informatique, Université Cheikh Anta Diop de Dakar UCAD, B.P. 5005, Dakar-Fann, Sénégal
  • 4. Institute of Mathematics and Physics, Department of Mathematics, University of Abomey-Calavi, 072 BP. 50, Cotonou, Benin Republic
  • 5. Departement de Physique, Universite de Lome, 01 BP 1515, Lomé, Togo
  • 6. International Centre for Research, and Advanced Studies in Mathematical & Computer Sciences, and Applications ICRASMCSA, 072 B.P. 50, Cotonou, Benin Republic

Description

Narayana's sequence is a ternary recurrent sequence defined by the recurrence relation [Formula: see text] with initial terms [Formula: see text] and [Formula: see text]. Let [Formula: see text] be a positive integer. In this study, it is proved that the [Formula: see text]th Narayana's number [Formula: see text] which is concatenations of three repdigits in base [Formula: see text] satisfies [Formula: see text]. Moreover,it is shown that the largest Narayana's number which is concatenations of three repdigits in base [Formula: see text] with [Formula: see text] is [Formula: see text].
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