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Journal articles on the topic 'Woodall Numbers'

Author: Grafiati

Published: 7 June 2025

Last updated: 2 August 2025

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1

P, Shanmudanantham, and Deepika T. "A Study on the Sum of 'm+1' Consecutive Woodall Numbers." Indian Journal of Science and Technology 16, no. 44 (2023): 3982–86. https://doi.org/10.17485/IJST/v16i44.2084.

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Abstract <strong>Objectives:</strong> 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. <strong>Methods:</strong> 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. <strong>Findings

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2

Eren, Orhan, and Yuksel Soykan. "Gaussian Generalized Woodall Numbers." Archives of Current Research International 23, no. 8 (2023): 48–68. http://dx.doi.org/10.9734/acri/2023/v23i8611.

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In this work, we define and investigate Gaussian generalized Woodall numbers in detail, and focus on four specific cases: Gaussian modified Woodall numbers, Gaussian modified Cullen numbers, Gaussian Woodall numbers, and Gaussian Cullen numbers. We present some identities and matrices related to these sequences, as well as recurrence relations, Binet’s formulas, generating functions, Simpson’s formulas, and summation formulas.

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3

Eren, Orhan, and Yuksel Soykan. "On Hyperbolic Generalized Woodall Numbers." Asian Journal of Advanced Research and Reports 18, no. 2 (2024): 43–69. http://dx.doi.org/10.9734/ajarr/2024/v18i2605.

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In this study, we introduce the generalized hyperbolic Woodall numbers. As special cases, we study with hyperbolic Woodall, hyperbolic modified Woodall, hyperbolic Cullen numbers and hyperbolic modified Cullen numbers. We present Binet’s formulas, generating functions and the summation formulas for these numbers. Besides, we give Catalan’s and Cassini’s identities and present matrices related to these sequences.

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4

Eren, Orhan, and Yuksel Soykan. "On Dual Hyperbolic Generalized Woodall Numbers." Archives of Current Research International 24, no. 11 (2024): 398–423. http://dx.doi.org/10.9734/acri/2024/v24i11981.

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In this work, we introduce the generalized dual hyperbolic Woodall numbers. As special cases, we study with dual hyperbolic Woodall, dual hyperbolic modified Woodall, dual hyperbolic Cullen numbers and dual hyperbolic modified Cullen numbers. Also, we present Binet’s formulas, generating functions, some identities, linear sums and matrices related with these sequences. In addition, we give Catalan’s and Cassini’s identities.

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5

Luca, Florian, and Igor E. Shparlinski. "Pseudoprime Cullen and Woodall numbers." Colloquium Mathematicum 107, no. 1 (2007): 35–43. http://dx.doi.org/10.4064/cm107-1-5.

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6

Azami, Kazuki, and Shigenori Uchiyama. "Primality testing of Woodall numbers." JSIAM Letters 6 (2014): 1–4. http://dx.doi.org/10.14495/jsiaml.6.1.

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7

Bérczes, Attila, István Pink, and Paul Thomas Young. "Cullen numbers and Woodall numbers in generalized Fibonacci sequences." Journal of Number Theory 262 (September 2024): 86–102. http://dx.doi.org/10.1016/j.jnt.2024.03.006.

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8

Shanmudanantham, P., and T. Deepika. "A Study on the Sum of ‘m+1’ Consecutive Woodall Numbers." Indian Journal Of Science And Technology 16, no. 44 (2023): 3982–86. http://dx.doi.org/10.17485/ijst/v16i44.2084.

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9

Akkuş, Hakan, Bahar Kuloğlu, and Engin Özkan. "Analytical Characterization of Self-Similarity in k-Cullen Sequences Through Generating Functions and Fibonacci Scaling." Fractal and Fractional 9, no. 6 (2025): 380. https://doi.org/10.3390/fractalfract9060380.

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In this study, we define the k-Cullen, k-Cullen–Lucas, and Modified k-Cullen sequences, and certain terms in these sequences are given. Then, we obtain the Binet formulas, generating functions, summation formulas, etc. In addition, we examine the relations among the terms of the k-Cullen, k-Cullen–Lucas, Modified k-Cullen, Cullen, Cullen–Lucas, Modified Cullen, k-Woodall, k-Woodall–Lucas, Modified k-Woodall, Woodall, Woodall–Lucas, and Modified Woodall sequences. The generating functions were derived and analyzed, especially for cases where Fibonacci numbers were assigned to parameter k. Graph

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10

FÜREDI, ZOLTAN, and DAVID S. GUNDERSON. "Extremal Numbers for Odd Cycles." Combinatorics, Probability and Computing 24, no. 4 (2014): 641–45. http://dx.doi.org/10.1017/s0963548314000601.

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We describe theC2k+1-free graphs onnvertices with maximum number of edges. The extremal graphs are unique forn∉ {3k− 1, 3k, 4k− 2, 4k− 1}. The value ofex(n,C2k+1) can be read out from the works of Bondy [3], Woodall [14], and Bollobás [1], but here we give a new streamlined proof. The complete determination of the extremal graphs is also new.We obtain that the bound forn0(C2k+1) is 4kin the classical theorem of Simonovits, from which the unique extremal graph is the bipartite Turán graph.

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11

Carolina, Sparavigna Amelia. "Composition Operations of Generalized Entropies Applied to the Study of Numbers." International Journal of Sciences Volume 8, no. 2019-04 (2019): 87–92. https://doi.org/10.5281/zenodo.3350673.

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The generalized entropies of C. Tsallis and G. Kaniadakis have composition operations, which can be applied to the study of numbers. Here we will discuss these composition rules and use them to study some famous sequences of numbers (Mersenne, Fermat, Cullen, Woodall and Thabit numbers). We will also consider the sequence of the repunits, which can be seen as a specific case of q-integers.Read Complete Article at ijSciences: V82019042044 AND DOI: http://dx.doi.org/10.18483/ijSci.2044

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12

Shanmuganandham, P., and R. Ramachandran. "A Study on the Sum of ‘m+1’ Consecutive Cullen Numbers." Indian Journal Of Science And Technology 17, no. 34 (2024): 3496–501. http://dx.doi.org/10.17485/ijst/v17i34.1696.

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Objectives: To discover new formulae for the matrix form of the sum of m+1 Cullen numbers. This is an effort to explain the Recursive Matrix form formula and a few of its uses. Methods: Conclusions derived from theorems and the matching matrix representations of them. Additionally, a few apps are offered. The terminology of Cullen Numbers are utilised to demonstrate the main theorems. Additionally, algebraic simplifications and mathematical computations are used to derive the findings. Findings: A lemma is used to construct the formula for the Sum of m+1 consecutive Cullen Numbers. Here, the r

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13

P, Shanmuganandham, and Ramachandran R. "A Study on the Sum of 'm+1' Consecutive Cullen Numbers." Indian Journal of Science and Technology 17, no. 34 (2024): 3496–501. https://doi.org/10.17485/IJST/v17i34.1696.

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Abstract <strong>Objectives:</strong> To discover new formulae for the matrix form of the sum of m+1 Cullen numbers. This is an effort to explain the Recursive Matrix form formula and a few of its uses. <strong>Methods:</strong> Conclusions derived from theorems and the matching matrix representations of them. Additionally, a few apps are offered. The terminology of Cullen Numbers are utilised to demonstrate the main theorems. Additionally, algebraic simplifications and mathematical computations are used to derive the findings. <strong>Findings:</strong> A lemma is use

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14

P, Shanmudanantham, and Deepa C. "A study on the sum of 'n+1' Consecutive Coral Numbers." Indian Journal of Science and Technology 16, no. 45 (2023): 4275–79. https://doi.org/10.17485/IJST/v16i45.2103.

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Abstract <strong>Objectives:</strong> To find new formulas for Sums of n+1 Coral Numbers and its matrix form. <strong>Methods:</strong> 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. <strong>Findings:</strong> A formula for the Sum of n+1 consecutive Coral numbers is obtained by employing a le

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15

Sparavigna, Amelia Carolina. "Some Groupoids and their Representations by Means of Integer Sequences." International Journal of Sciences 8, no. 10 (2019): 1–5. https://doi.org/10.18483/ijSci.2188.

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In some previous works, we have discussed the groupoids related to the integer sequences of Mersenne, Fermat, Cullen, Woodall and other numbers. These groupoids possess different binary operators. As we can easily see, other integer sequences can have the same binary operators, and therefore can be used to represent the related groupoids. Using the On-Line Encyclopedia of Integer Sequences (OEIS), we are able to identify the properties of these representations of groupoids. At the same time, we can also find integer sequences not given in OEIS and probably not yet studied.

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16

Carolina, Sparavigna Amelia. "Some Groupoids and their Representations by Means of Integer Sequences." International Journal of Sciences Volume 8, no. 2019-10 (2019): 1–5. https://doi.org/10.5281/zenodo.3979993.

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Abstract:

In some previous works, we have discussed the groupoids related to the integer sequences of Mersenne, Fermat, Cullen, Woodall and other numbers. These groupoids possess different binary operators. As we can easily see, other integer sequences can have the same binary operators, and therefore can be used to represent the related groupoids. Using the On-Line Encyclopedia of Integer Sequences (OEIS), we are able to identify the properties of these representations of groupoids. At the same time, we can also find integer sequences not given in OEIS and probably not yet studied.Read Complete Article

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17

Chen, Rong, and Zijian Deng. "Seymour and Woodall’s Conjecture Holds for Graphs with Independence Number Two." SIAM Journal on Discrete Mathematics 39, no. 2 (2025): 1096–101. https://doi.org/10.1137/24m1666768.

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18

Shanmuganandham, P., and T. Deepika. "Sum of Squares of ‘m’ Consecutive Woodall Numbers." Baghdad Science Journal 20, no. 1(SI) (2023). http://dx.doi.org/10.21123/bsj.2023.8409.

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This paper discusses the Sums of Squares of “m” consecutive Woodall Numbers. These discussions are made from the definition of Woodall numbers. Also learn the comparability of Woodall numbers and other special numbers. An attempt to communicate the formula for the sums of squares of ‘m’ Woodall numbers and its matrix form are discussed. Further, this study expresses some more correlations between Woodall numbers and other special numbers.

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19

Janaki, G., and S. Shanmuga Priya. "Relationship between Pythagoren Triangles & Woodall Primes." INTERANTIONAL JOURNAL OF SCIENTIFIC RESEARCH IN ENGINEERING AND MANAGEMENT 07, no. 04 (2023). http://dx.doi.org/10.55041/ijsrem18940.

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In this article, we focus on generating the Pythogoren triangles using Woodall prime numbers by equating the ratio Area/Perimeter to different woodall prime numbers. Of these, a few interesting patterns are displayed. Key Words: Pythagorean Triangle, Woodall prime number.

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20

SOYKAN, Yüksel, and Vedat İRGE. "Generalized Woodall Numbers: An Investigation of Properties of Woodall and Cullen Numbers via Their Third Order Linear Recurrence Relations." Universal Journal of Mathematics and Applications, June 30, 2022, 69–81. http://dx.doi.org/10.32323/ujma.1057287.

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In this paper, we investigate the generalized Woodall sequences and we deal with, in detail, four special cases, namely, modified Woodall, modified Cullen, Woodall and Cullen sequences. We present Binet's formulas, generating functions, Simson formulas, and the summation formulas for these sequences. Moreover, we give some identities and matrices related with these sequences.

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21

Fan, Dandan, and Huiqiu Lin. "Binding Number, $k$-Factor and Spectral Radius of Graphs." Electronic Journal of Combinatorics 31, no. 1 (2024). http://dx.doi.org/10.37236/12165.

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The binding number $b(G)$ of a graph $G$ is the minimum value of $|N_{G}(X)|/|X|$ taken over all non-empty subsets $X$ of $V(G)$ such that $N_{G}(X)\neq V(G)$. The association between the binding number and toughness is intricately interconnected, as both metrics function as pivotal indicators for quantifying the vulnerability of a graph. The Brouwer-Gu Theorem asserts that for any $d$-regular connected graph $G$, the toughness $t(G)$ always at least $\frac{d}{\lambda}-1$, where $\lambda$ denotes the second largest absolute eigenvalue of the adjacency matrix. Inspired by the work of Brouwer an

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22

Duellman, Kasia M., Melinda A. Lent, Lara Brown, Miranda Harrington, Stephanie Harrington, and James Warwick Woodhall. "First report of rubbery rot of potato caused by Geotrichum candidum in the United States." Plant Disease, December 2, 2020. http://dx.doi.org/10.1094/pdis-08-20-1815-pdn.

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Rubbery rot of potato caused by Geotrichum candidum Link is characterized by symptoms of damp, flaccid tubers that feel rubbery when squeezed (Humpreys-Jones 1969), similar in consistency to potato diseases such as pink rot (caused by Phytophthora erythroseptica) and Pythium leak (caused by species of Pythium). In November 2019, several symptomatic tubers of potato variety ‘Ciklamen’ that had been held in storage since harvest and originated from an over-head irrigated, sandy-loam production field in Bingham county, Idaho were submitted to the University of Idaho for diagnosis. Shipping-point

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