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Integer sequences
Results: 1364

#	Item
901	Bernoulli numbers and generalized factorial sums Paul Thomas Young Department of Mathematics, College of Charleston Charleston, SC[removed]removed] Add to Reading List Source URL: youngp.people.cofc.edu Language: English - Date: 2010-06-25 15:31:33 Combinatorics Modular arithmetic Bernoulli number Topology Bernoulli polynomials Binomial coefficient P-adic number Summation Factorial Mathematics Number theory Integer sequences
902	UIUC Mock Putnam Exam[removed]Solutions Problem 1. Without any numerical calculations, determine which of the two numbers eπ and π e is larger. Solution. Let a = eπ and b = π e . We will show that a > b. Since Add to Reading List Source URL: www.math.illinois.edu Language: English - Date: 2005-10-11 15:50:00 Integer sequences Polynomial Exponentiation Logarithm Pi Factorial Proof that π is irrational Binomial coefficient Mathematics Mathematical analysis Combinatorics
903	UIUC Mock Putnam Exam[removed]Problem 1. Without any numerical calculations, determine which of the two numbers eπ and π e is larger. Problem 2. Prove that, given any set of 10 distinct positive integers Add to Reading List Source URL: www.math.illinois.edu Language: English - Date: 2005-10-06 17:16:27 Transcendental numbers Combinatorics Integer sequences Decimal representation Pi Floating point Integer Factorial E Mathematics Elementary mathematics Number theory
904	U OF I MOCK PUTNAM EXAM SEPT. 29, [removed]Suppose P (x) is a polynomial with integer coefficients such that none of the values P (1), . . . , P[removed]is divisible by[removed]Prove that P (n) 6= 0 for all integers n. 2. Fi Add to Reading List Source URL: www.math.illinois.edu Language: English - Date: 2009-09-30 19:05:13 Algebraic number theory Integer sequences Elementary number theory Integer Ring theory Number Square-free integer Binomial coefficient Mathematics Abstract algebra Number theory
905	UIUC Mock Putnam Exam[removed]Solutions Problem 1. Let a1 = 1, a2 = 1, a3 = −1, and for n > 3 define an by an = an−1 an−3 . Find a2006 . Solution. Computing the first 10 terms of the sequence {an }, we obtain Add to Reading List Source URL: www.math.illinois.edu Language: English - Date: 2006-10-08 16:27:20 Fibonacci number Summation Mathematical induction Factorial Recurrence relation Generating function Binomial coefficient Formal power series Mathematics Combinatorics Integer sequences
906	R Recent and Noteworthy Sequences in the OEIS⃝ N. J. A. Sloane, The OEIS Foundation Inc., 11 South Adelaide Avenue, Highland Park, NJ 08904, USA, Add to Reading List Source URL: neilsloane.com Language: English - Date: 2012-12-18 14:30:29 Integer sequences Polynomials On-Line Encyclopedia of Integer Sequences Expected value Quasigroup Mathematics Abstract algebra Mathematical analysis
907	Study sheet for Final CS1100 by Matt in Wed night class Licensed under the GNU Free Documentation License (GFDL) http://www.gnu.org/copyleft/fdl.html Sequences – have patterns; possible patterns are: 1. Term related to Add to Reading List Source URL: www.ping127001.com Language: English - Date: 2007-12-26 20:33:36 Number theory Combinatorics Complex analysis Mathematical series Summation Logical connective Pi Factorial Bernoulli number Mathematics Mathematical analysis Integer sequences
908	U OF I MOCK PUTNAM EXAM SEPT. 29, 2008 Solutions 1. A sequence a0 , a1 , a2[removed]of real numbers is defined recursively by an (n = 0, 1, 2, . . .). Add to Reading List Source URL: www.math.illinois.edu Language: English - Date: 2008-10-01 17:30:45 Exponentials Exponentiation Factorial Mathematics Combinatorics Integer sequences
909	Coconut Divisibility Problem Brian Rothstein November 1, 2000 1 Add to Reading List Source URL: www.ugcs.caltech.edu Language: English - Date: 2007-09-20 19:32:04 Integer factorization algorithms Modular arithmetic Combinatorics Mathematics Number theory Integer sequences
910	Rational series for multiple zeta and log gamma functions Paul Thomas Young Department of Mathematics College of Charleston Charleston, SC 29424, USA Add to Reading List Source URL: youngp.people.cofc.edu Language: English - Date: 2013-08-19 21:49:23 Number theory Integer sequences Meromorphic functions Special functions Analytic number theory Bernoulli number Bernoulli polynomials Gamma function Riemann zeta function Mathematics Mathematical analysis Complex analysis

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