List of abstracts of the papers that appeared in "Topics in Recreational Mathematics Volume 8" edited by Charles Ashbacher

List of abstracts of the papers that appeared in "Topics in Recreational Mathematics Volume 8" edited by Charles Ashbacher 

List of abstracts of the papers that appeared in Topics in Recreational Mathematics Volume 8  edited by Charles Ashbacher, ISBN 978-1537333212

Nonamorphic Numbers Revisited

Charles Ashbacher

cashbacher@yahoo.com

Abstract

 In volume 20, number 2 of Journal of Recreational Mathematics, Charles W. Trigg defined a nonamorphic number to be a nonagonal number N(n) = n(7n – 5) / 2 that terminates in n. For example, N(25) = 2125 and N(625) = 1365625. The purpose of this paper is to report the results of a greater search for nonamorphic numbers.

Octamorphic Numbers Revisited

Charles Ashbacher
cashbacher@yahoo.com

Abstract

 In volume 19, number 2 of Journal of Recreational Mathematics, Charles W. Trigg defined an octamorphic number to be an octagonal number E(n) = n(3n – 2) that terminates in n. For example, E(25) = 1825 and E(625) = 1170625. The purpose of this paper is to report the results of a greater search for octamorphic numbers.

Pentamorphic Numbers Revisited

Charles Ashbacher

cashbacher@yahoo.com

Abstract

 In volume 16, number 1 of Journal of Recreational Mathematics, Charles W. Trigg defined a pentamorphic number to be a pentagonal number P(n) = n(3n – 1) / 2 that terminates in n. For example, P(25) = 925 and P(625) = 585625. The purpose of this paper is to report the results of a greater search for pentamorphic numbers.

African Horizons: A Math Enrichment Experience in Kenya

Lamarr Widmer

Messiah College

widmer@messiah.edu

Abstract

 The author’s most recent teaching experience in Africa was one year of teaching mathematics at Daystar University.  This paper describes challenges with the classroom culture at that institution and the author’s attempt to motivate students through the use of mathematical activity of a more recreational nature.

The Life-Time of the World

A.A.K. Majumdar

APU, 1-1 Jumonjibaru, Beppu-shi 874-8577, Japan

majumdar@apu.ac.jp

Abstract

 The legend is that, at the creation of the world, there was a Tower of Hanoi with three poles and 64 discs, in a temple. The priests there are in the process of transferring the tower from one pole to another, in minimum number of moves, where each move transfers one disc from one pole to another under the “divine rule” that no disc can ever be placed on top of a smaller one. As soon as the task of the priests would be completed, the world would come to an end. This paper examines the different cases when a single relaxation of the “divine rule” is allowed.

Keywords. The Tower of Hanoi, divine rule, the life-time of the world.

Palindromic Numbers and Iterations of the Pseudo-Smarandache Function

Charles Ashbacher

cashbacher@yahoo.com

Abstract

 For n ≥ 1, the Pseudo-Smarandache function Z(n) is the smallest integer m such that n evenly divides  1 + 2 + 3 + . . . + m. In this paper, some iterations of this function on palindromes that yield palindromes are demonstrated.

 This paper was originally published in Proceedings of the First International Conference on Smarandache Type Notions in Number Theory, American Research Press, 1997.
ISBN 1-879585-58-8.

Divisibility and Periodicity Patterns and Palatable Number Tricks in the Jacobsthal Sequence

Jay L. Schiffman

Rowan University

schiffman@rowan.edu

Abstract

The Jacobsthal sequence is a Fibonacci-like sequence defined as follows:

            J₀ = 0, J₁ = 1 and J_n = J_n-1 + 2 * J_n-2 for n  ≥ 2.

The initial few terms of this sequence are 0, 1, 1, 3, 5, 11, 21, 43, 85,…. This paper will explore divisibility and periodicity patterns, early primes and palatable number tricks in this sequence.

Smarandache Bisymmetric Geometric Determinant Sequence

A.A.K. Majumdar

APU, 1–1 Jumonjibaru, Beppu-shi 875–8577, Oita-ken, Japan

majumdar@apu.ac.jp/aakmajumdar@gmail.com

Abstract

In this paper, the concept of Smarandache bisymmetric geometric determinant sequence has been introduced. An explicit form of the n^th term is given.

Key Words  Smarandache bisymmetric geometric determinant sequence, n^th term of the sequence.

The NFL Draft, 2002-2014: Winners, Losers, and  a
New Draft Trade Value Chart

Paul M. Sommers

Middlebury College

psommers@middlebury.edu

Abstract

 Data on career approximate value (AV) of all National Football League (NFL) players drafted between 2002 and 2014 show how career AV varies by round, position, and team.  Career AVs of the drafted players are then used to assess winners and losers in each of the thirteen annual NFL drafts.  Finally, regression analysis is employed to assign a trade value to each of the 224 players picked in a 32-team, seven-round draft.  These values are used to evaluate the draft day trades in 2010 and which teams stand to benefit from trades up to and during the 2015 NFL draft.