On Generalized p-Mersenne Numbers

Soykan, Yüksel

doi:10.34198/ejms.8122.83120

Cited by 5 publications

(4 citation statements)

References 21 publications

(21 reference statements)

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“…The sums of squares of generalized Fibonacci number and Tribonacci number [2][3][4] . Likewise, a study on Generalized Mersenne numbers by Soykan Y 5 . Now look into sums of squares of 'm' consecutive carol numbers and its matrices representation starting with 7, every third carol numbers is multiple of 7.…”

Section: Introductionmentioning

confidence: 99%

Sum of Squares of ‘n’ Consecutive Carol Numbers

SHANMUGANANDHAM

DEEPA²

2023

Baghdad Sci.J

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Section: Introductionmentioning

confidence: 99%

Sum of Squares of ‘n’ Consecutive Carol Numbers

SHANMUGANANDHAM

DEEPA²

2023

Baghdad Sci.J

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“…The generalized Mersenne number has been introduced and dealt with two special cases, namely, Mersenne and Mersenne-Lucas sequences (10) . They discussed the Binet's formulas, generating functions, Simson formulas, and the summation formulas for these sequences.…”

Section: Introductionmentioning

confidence: 99%

A study on the sum of ‘n+1’ Consecutive Coral Numbers

Shanmudanantham,

Deepa

2023

IJST

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Objectives: To find new formulas for Sums of n+1 Coral Numbers and its matrix form. Methods: Here an attempt made to communicate the formula for Recursive Matrix form and some of its applications. If applications are also provided. Moreover results are obtained by employing mathematical calculations and algebraic simplifications. Results are established by main theorems and their corollary and matrix representations. Findings: A formula for the Sum of n+1 consecutive Coral numbers is obtained by employing a lemma. Matrix form for the sum and Recursive forms are attained here. The matrix form of sums of n+1 consecutive Cullen Numbers is also gained. In the application part some interesting associations between Special Numbers, Cullen Numbers and Carol Numbers are given. Novelty: In the analysis, entirely new formulae are procured. Matrix representation and its recursive forms are new finding in the area of research. Also, different types of correlations between Carol Numbers and other special numbers are provided.

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“…The Mersenne and Mersenne-Lucas sequences have been discussed as two particular examples of the generalized Mersenne number (9) . They spoke about the generating functions, Simson formulae, Binet formulas, and summation formulas for these sequences.…”

Section: Introductionmentioning

confidence: 99%

A Study on the Sum of ‘m+1’ Consecutive Woodall Numbers

Shanmudanantham,

Deepika

2023

IJST

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Objectives: The Objective of this article is to find new formulas for Sums of m+1 Woodall Numbers and its matrix form. Here an attempt made to communicate the formula for Recursive Matrix form and some of its applications. Methods: Theorems are proved using the definitions of Woodall numbers. Some applications are also provided. Moreover, results are obtained by employing mathematical calculations and algebraic simplifications. Results are established by main theorems and their corollary and matrix representations. Findings: A formula for the Sum of m+1 consecutive Woodall numbers is obtained by utilizing a lemma. Matrix form for the sum and Recursive forms are attained here. The matrix form of sums of m+1 consecutive Cullen Numbers is also gained. In the application part some interesting associations between Special Numbers, Cullen Numbers and Carol Numbers are given. Novelty: In the analysis, entirely new formulae are procured. Matrix representation and its recursive forms are new finding in the area of research. Also, different types of correlations between Woodall Numbers and other special numbers are provided.

show abstract

On Generalized p-Mersenne Numbers

Cited by 5 publications

References 21 publications

Sum of Squares of ‘n’ Consecutive Carol Numbers

Sum of Squares of ‘n’ Consecutive Carol Numbers

A study on the sum of ‘n+1’ Consecutive Coral Numbers

A Study on the Sum of ‘m+1’ Consecutive Woodall Numbers

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