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Every hexagonal number is a triangular number, but only every other triangular number (the 1st, 3rd, 5th, 7th, etc.) is a hexagonal number. Like a triangular number, the digital root in base 10 of a hexagonal number can only be 1, 3, 6, or 9. The digital root pattern, repeating every nine terms, is "1 6 6 1 9 3 1 3 9". Every even perfect number ...
Centered hexagonal numbers appearing in the Catan board game: 19 land tiles, 37 total tiles. In mathematics and combinatorics, a centered hexagonal number, or centered hexagon number, [1] [2] is a centered figurate number that represents a hexagon with a dot in the center and all other dots surrounding the center dot in a hexagonal lattice.
This is the minimum number of characters needed to encode a 32 bit number into 5 printable characters in a process similar to MIME-64 encoding, since 85 5 is only slightly bigger than 2 32. Such method is 6.7% more efficient than MIME-64 which encodes a 24 bit number into 4 printable characters. 89
Number Multiplier Number Multiplier 1 mono- 30 triaconta- 2 di- 31 hentriaconta- 3 tri- 32 dotriaconta- 4 tetra- 33 tritriaconta- 5 penta- 34 tetratriaconta- 6 hexa- 40 tetraconta- 7 hepta- 50 pentaconta- 8 octa- 60 hexaconta- 9 nona- 70 heptaconta- 10 deca- 80 octaconta- 11 undeca- 90 nonaconta- 12 dodeca- 100 hecta- 13 trideca- 200 dicta- 14
Another common way of expressing the base is writing it as a decimal subscript after the number that is being represented (this notation is used in this article). 1111011 2 implies that the number 1111011 is a base-2 number, equal to 123 10 (a decimal notation representation), 173 8 and 7B 16 (hexadecimal).
For example, "11" represents the number eleven in the decimal or base-10 numeral system (today, the most common system globally), the number three in the binary or base-2 numeral system (used in modern computers), and the number two in the unary numeral system (used in tallying scores). The number the numeral represents is called its value.
This gnomonic technique also provides a mathematical proof that the sum of the first n odd numbers is n 2; the figure illustrates 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 = 64 = 8 2. There is a similar gnomon with centered hexagonal numbers adding up to make cubes of each integer number.
This is exactly the general form of a centered hexagonal number; that is, all of these cuban primes are centered hexagonal. As of July 2023 [update] the largest known has 3,153,105 digits with y = 3 3304301 − 1 {\displaystyle y=3^{3304301}-1} , [ 2 ] found by R.Propper and S.Batalov.