My search for patterns continues.  Patterns in nature, patterns in numbers, patterns in everything, patterns everywhere. The date of this dream was not recorded due to procrastination.   In this dream I saw phone numbers with the following anatomy:

(315) xxx xxxx, (918) 367 – 2210

The area code 315 belongs to the city of Syracuse in the state of New York. Unfortunately, I did not remember the rest of the seven digits. On the other hand, the area code 918 belongs to Tulsa county, one of the 72 counties in the state of Oklahoma. As I checked the Oklahoma State Department of Education School Directory, I found out that (918) 367 – 2210 belongs to Caddo Public Schools in Tulsa County.  As I took a closer look at the area code 315, and the number 367 in the second phone number, some interesting and surprising patterns started to emerge. Look at the following:

Sum of First And Third Digits

In each of the numbers 315 and 367, the sum of the first and third digit is an even number.

3 + 5 = 8, 3 + 7 = 10.

Not only that.

These sums are not only even, they are also consecutive.

In 315 and 367, the sum of second and third digits is a square number

i.e. 3 + 1 = 4, 3 + 6 = 9 and 4 and 9 are consecutive square numbers.

Product of First And Third Digits

In 315 and 367, the product of the first and third digit is a triangular number i.e. 3×5 = 15 , 3×7 = 21 and 15 and 21 are consecutive triangular numbers.

Sum of Digits

Also in 315 and 367, the sum of the digits is equal to a square number

i.e. 3 + 1 + 5 = 9 , 3 + 6 + 7 = 16

and 9 and 16 are consecutive square numbers

i.e. 3^2 = 9, 4^2 = 16

Describing the Third Digits

Each of the numbers has 3 as its third digit while 315 and 367 end with the odd numbers 5 and 7 respectively which are again consecutive. This is all amazing.  Isn’t it ?

Checking for Degree of Correspondence

Since this dream I have written a book on the subject of triangular numbers titled, A Course in Triangular Numbers.  Triangular numbers, it should be recalled are numbers of the form:  1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190…

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