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The maximum number of pieces from consecutive cuts are the numbers in the Lazy Caterer's Sequence. When a circle is cut n times to produce the maximum number of pieces, represented as p = f (n), the n th cut must be considered; the number of pieces before the last cut is f (n − 1), while the number of pieces added by the last cut is n.
1 is read off as "one 1" or 11. 11 is read off as "two 1s" or 21. 21 is read off as "one 2, one 1" or 1211. 1211 is read off as "one 1, one 2, two 1s" or 111221. 111221 is read off as "three 1s, two 2s, one 1" or 312211. The look-and-say sequence was analyzed by John Conway [1] after he was introduced to it by one of his students at a party. [2 ...
A graph-based algorithm that constructs a graph of the sequence. no [11] SubSeqer: 2008 web: A graph-based approach for the detection and identification of repetitive elements in low–complexity sequences. no [12] ANNIE: 2009 web: This method creates an automation of the sequence analytic process. no [13] LPS-annotate 2011 on request
The sequence 2, 1, 3, 4, 7, 11, ... of Lucas numbers satisfies the same recurrence as the Fibonacci sequence but with initial conditions = and =. More generally, every Lucas sequence is constant-recursive of order 2.
Borrowing costs on 15-year fixed-rate mortgages, popular with homeowners seeking to refinance their home loan to a lower rate, also eased this week. The average rate fell to 5.96% from 6.1% last week.
Name First elements Short description OEIS Mersenne prime exponents : 2, 3, 5, 7, 13, 17, 19, 31, 61, 89, ... Primes p such that 2 p − 1 is prime.: A000043 ...
From May 2008 to August 2012, if you bought shares in companies when W.R. Rhodes joined the board, and sold them when he left, you would have a -37.6 percent return on your investment, compared to a -2.4 percent return from the S&P 500.
Small business owners face severe penalties if they don't report to the federal government by year's end. Thousands of businesses may not realize they are subject to a new reporting process ...