# Category Archives: Numbers

## A Mathematical Limerick

A mathematical limerick is truly a thing of beauty. $$\displaystyle{\frac{12 + 144 + 20 + 3\times\sqrt{4}}{7}} + 5\times11 = 9^{2} + 0$$ A dozen, a gross, and a score Plus three times the square root of four Divided by seven Plus five times eleven Is nine squared and not a bit more.

## If the Sum of the Digits of a Number is Divisible by Three, the Number Is Divisible by Three

Take a two-digit base-10 number where the digits are represented by ab. This number is equal to 10a + b and the sum of its digits are a + b. The difference between the number and the sum is 9a, which is divisible by three. So a + b is divisible by three, if and only… Read More »

## Can You Find Three Digits for A, B and C Such That ABC in Base-10 Is Equal to CBA in Base-9?

The only 3-digit answer is $$544_9 = 445_{10}$$. However, there are answers in other bases: $$211_3 = 112_4$$ $$322_5 = 223_6$$ $$433_7 = 334_8$$ $$544_9 = 445_{10}$$ Are you seeing a pattern here? Does the pattern extended to bases higher than 10? Does $$655_{10} = 556_{11}$$? Does $$766_{11} = 667_{12}$$? Cheating a little bit by… Read More »

## What comes next in the sequence 2, 3, 7, 23, …?

Somebody asked this question on Quora. I thought I’d give it a try. The next number is 37. This is a list of prime numbers whose English names have a prime number of letters. Note: This counts letters only, not hyphens or spaces. Number Spelling Letters 2 two 3 3 three 5 7 seven 5… Read More »

## Converting Between Julian Dates and Gregorian Calendar Dates in Fortran (and JavaScript)

When looking through some of my old papers I found at my father’s house after he died, I found some old Fortran code for converting Gergorian calendar dates to and from Julian dates. I haven’t used Fortran since the 1970s, so the code looked a little strange. Some examples of Julian dates: Julian Date Equivalent… Read More »

## Truncating Numbers in JavaScript

I needed a function to truncate a number. Math.floor() worked … until I tried it on a negative number. So I had to write my own truncate function. Even though I needed to truncate numbers to the integer portion only, I figured sooner or later I would need to truncate to a given number of… Read More »

## Telephone Exchange Names

This article is still being worked on, but I wanted to share it before it was completed. If you want to be notified when it is updated leave a comment below. When I was a child I lived in San Bernardino, California from 1966 to 1969. I can still remember my home telephone number: TUrner… Read More »

## Palindromic Prime Numbers, Part 2

So the question was asked on this page, “Are there any four-digit prime numbers?” Stop here and go to the other page if you want to read the first part about palindromic prime numbers and try to answer the question before reading the answer below. You’re still here, so here’s the answer. No. There are… Read More »

## Palindromic Prime Numbers, Part 1

A palindrome /ˈpælɪndroʊm/ is a word, phrase, number, or any other sequence of units which reads the same forwards as it does backwards. Examples of palindromes are the words sees, radar, madam, and aibohphobia (fear of palindromes); the sentences, “Rise to vote sir”, “Too hot to hoot”, “A war at Tarawa!”, and “Noel sees Leon”;… Read More »

## The Number 83

Miscellaneous 83 is the atomic number of bismuth (symbol Bi). In Judaism, when someone reaches 83 years old they may celebrate a second bar mitzvah. The Torah says that a normal lifespan is 70 years, so an 83-year-old person can be considered 13 years old in a second lifetime. 83 is the highest UHF channel… Read More »