A cyclic number is an integer for which cyclic permutations of the digits are successive integer multiples of the number. The most widely known is the six-digit number 142857, whose first six integer multiples are
142857 × 1 = 142857
142857 × 2 = 285714
142857 × 3 = 428571
142857 × 4 = 571428
142857 × 5 = 714285
142857 × 6 = 857142
== Details ==
To qualify as a cyclic number, it is required that consecutive multiples be cyclic permutations. Thus, the number 076923 would not be considered a cyclic number, because even though all cyclic permutations are multiples, they are not consecutive integer...
5
Yes, there are a few faster ways to make Langford sequences.
Firstly, here's a fairly simple way. Rather than testing all of the permutations containing the pairs of numbers from 1 to n, we generate the permutations of numbers from 1 to n and then try to build Langford sequences from those permu...
In combinatorics and in experimental design, a Latin square is an n × n array filled with n different symbols, each occurring exactly once in each row and exactly once in each column. An example of a 3×3 Latin square is
The name "Latin square" was inspired by mathematical papers by Leonhard Euler (1707–1783), who used Latin characters as symbols, but any set of symbols can be used: in the above example, the alphabetic sequence A, B, C can be replaced by the integer sequence 1, 2, 3. Euler began the general theory of Latin squares.
== History ==
The Korean mathematician Choi Seok-jeong was the...
8
Automatically generated gravatars, for SE users without their own profile picture, used to have 4-fold rotational symmetry. Some time recently, there's been a very subtle change and they now have reflectional symmetry in the y-axis instead. They haven't changed much, but I notice it every time I ...
19
