Magic Square of the Sun

Prime Numbers up to 100

Mayan Numerals based on a system of 20

Acrophonic Greek Numerals

Cyrillic Numerals

These are all prime numbers:
31
331
3331
33331
333331
3333331
33333331

0 x 9 + 8 = 8
9 x 9 + 7 = 88
98 x 9 + 6 = 888
987 x 9 + 5 = 8888
9876 x 9 + 4 = 88888
98765 x 9 + 3 = 888888
987654 x 9 + 2 = 8888888
9876543 x 9 + 1 = 88888888
98765432 x 9 + 0 = 888888888
987654321 x 9 - 1 = 8888888888
9876543210 x 9 - 2 = 88888888888

An unusual number or n  rough number n is an integer with a greatest prime factor exceeding n  For example, the greatest prime factor of 102 is 17, which is greater than 11 (the square root of 102 rounded up to the next higher integer). The first few unusual numbers are 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19, 20, 21, 22, 23, 26, 28, 29, 31, 33, 34, 35, 37, 38, 39, 41, 42, 43, 44, 46, 47, etc., listed in A064052 of Sloane's OEIS. In fact, Donald Knuth and Donald Greene, who coined the term ``unusual number,'' remark that these numbers occur so frequently they're not all that unusual. Unusual numbers include all of the prime numbers and many composites. Richard Schroeppel proved in HAKMEM 239 that the probability that a random integer is unusual is log2 (about 0.69314718).

Psychic and Destiny Number Generator:

The Unicursal Hexagram is a hexagram or six sided and six pointed star that is unique in that it can be traced or drawn as one complete symbol, rather than two overlaid triangles. This is significant as the triangles are often used to represent opposites such as fire and water or male and female. The unifying of the symbol into one represents the union of opposites. A hexagram (also known as sexagram or a magician's/sorcerer's star) is a six-pointed star, a type of complex star polygon. The Unicursal Hexagram is so-called because it can be drawn unicursally - that is, in one continuous movement.

A circuit in which an entire graph is traversed in one route. Examples of curves that can be traced unicursally are the Mohammed sign and unicursal hexagram.

The numbers of distinct unicursal polygrams that can be formed from n points on circle with no two adjacent for n=1, 2, ... are 1, 0, 0, 0, 1, 3, 23, 177, 1553, ... (Sloane's A002816). For n>2, these are given by the sum a(n)=(-1)^n+1/2(n-1)!+sum_(k=1)^(n-1)sum_(j=1)^k((-1)^k2^(j-1)(k-1; j-1)(n-k; j)n(n-k-1)!)/(n-k).

This sequence is also given by the recurrence equation
(n^2-7n+9)a(n)=(n-5)(n^2-5n+3)a(n-5)+(n^2-7n+9)a(n-4)-2(n-6)(n^2-5n+3)a(n-3) +(n^3-8n^2+18n-21)a(n-1)+4(n-5)na(n-2).

SEE ALSO: Circuit, Eulerian Circuit, Hexagram, Königsberg Bridge Problem, Mohammed Sign, Traceable Graph

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