Number 14 in Math

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 Number 14 in Math.    Number 14

 

A pyramidal number (sum of all squares of integers from 1 to 3): 14 = 12+22+32.

 

14×82 = 1,148 = 41×28.

 

147 = 142–72 = (14+7)×7, where 14 = 7×2.

 

The first Keith number: 1, 4, 5, 9, 14, 23…

 

Squares of 2 consecutive numbers that use the same digits: 132 = 169 and 142 = 196. Others: 1572 & 1582 and 9132 & 9142.

 

Three square numbers using the same digits: 132 = 169, 142 = 196 and 312 = 961.

 

A Catalan number: C4 = 14. (There are 14 ways to cut a hexagon into 4 triangles).

 

1×7 + 3 = 10

14×7 + 2 = 100

142×7 + 6 = 1000

1428×7 + 4 = 10000

14285×7 + 5 = 100000

142857×7 + 1 = 1000000

 

1428571×7 + 3 = 10000000

14285714×7 + 2 = 100000000

142857142×7 + 6 = 1000000000

1428571428×7 + 4 = 10000000000

14285714285×7 + 5 = 100000000000

142857142857×7 + 1 = 1000000000000

 

1428571428571×7 + 3 = 10000000000000