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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.
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 ...
DABACABA patterns in (3-bit) binary numbersThe ABACABA pattern is a recursive fractal pattern that shows up in many places in the real world (such as in geometry, art, music, poetry, number systems, literature and higher dimensions).
In the case of the lazy caterer's sequence, the maximum number of pieces you can cut a pancake into with n cuts, the OEIS gives the sequence as 1, 2, 4, 7, 11, 16, 22, 29, 37, ... A000124, with offset 0, while Mathworld gives the sequence as 2, 4, 7, 11, 16, 22, 29, 37, ... (implied offset 1).
The 2014–15 Euro Hockey Tour was the 19th season of Euro Hockey Tour. It started on 6 November 2014 and finished on 25 April 2015. It started on 6 November 2014 and finished on 25 April 2015. A total of 24 games were played, with each team playing 12 games.
Given four indices i 1 ≤ i 2 and j 1 ≤ j 2, the set E(i 1,i 2,j 1,j 2) contains the indices of all rectangles whose bottom-left corner is in the rectangle [x i 1,x i 2] X [y p (j1),y p (j2)]. A cutting pattern is a guillotine pattern if and only if, for all quadruplets of indices i 1 ≤ i 2 and j 1 ≤ j 2, at least one of the following ...
In combinatorial mathematics and theoretical computer science, a (classical) permutation pattern is a sub-permutation of a longer permutation.Any permutation may be written in one-line notation as a sequence of entries representing the result of applying the permutation to the sequence 123...; for instance the sequence 213 represents the permutation on three elements that swaps elements 1 and 2.
They have a variety of color schemes and measure from 120 by 62 millimetres (4.7 in × 2.4 in) to 160 by 82 millimetres (6.3 in × 3.2 in) (first series) and from 120 by 62 millimetres (4.7 in × 2.4 in) to 153 by 77 millimetres (6.0 in × 3.0 in) (second series).