Do the digits of n alternate in the form abab In this case, a = 1 and b = 9 In order to be undulating, Digit 1: 111 should be equal to 1 In order to be undulating, Digit 2: 999 should be equal to 9 In order to be undulating, Digit 3: 111 should be equal to 1 Since all 3 digits form our abab undulation pattern 191 is undulating
Is there a number m such that m2 = n 132 = 169 and 142 = 196 which do not equal 191 Therefore, 191 is not a square
Is there a number m such that m3 = n 53 = 125 and 63 = 216 ≠ 191 Therefore, 191 is not a cube
Is the number read backwards equal to the number? The number read backwards is 191 Since 191 is the same backwards and forwards it is a palindrome
Palindromic Prime Test:
Is it both prime and a palindrome From above, since 191 is both prime and a palindrome it is a palindromic prime
A number is repunit if every digit is equal to 1 Since there is at least one digit in 191 ≠ 1 then it is NOT repunit
Apocalyptic Power Test:
Does 2n contains the consecutive digits 666. 2191 = 3.1385508676933E+57 Since 2191 does not have 666 191 is NOT an apocalyptic power
It satisfies the form:
n(3n - 1)
Check values of 11 and 12
Using n = 12, we have:
12(3(12 - 1)
12(36 - 1)
210 ← Since this does not equal 191 this is NOT a pentagonal number
Using n = 11, we have:
11(3(11 - 1)
11(33 - 1)
176 ← Since this does not equal 191 this is NOT a pentagonal number
220 ← Since this does not equal 191 This is NOT a tetrahedral (Pyramidal) number
Using n = 9, we have:
9(9 + 1)(9 + 2)
165 ← Since this does not equal 191 This is NOT a tetrahedral (Pyramidal) number
Narcissistic (Plus Perfect) Test:
Is equal to the square sum of it's m-th powers of its digits 191 is a 3 digit number, so m = 3 Square sum of digitsm = 13 + 93 + 13 Square sum of digitsm = 1 + 729 + 1 Square sum of digitsm = 731 Since 731 <> 191 191 is NOT narcissistic (plus perfect)
C6 = 132 Since this does not equal 191 This is NOT a Catalan number
Property Summary for the number 191
· Positive · Whole · Prime · Deficient · Odd · Odious · Undulating · Palindrome · Palindromic Prime
What is the Answer?
Positive Whole Prime Deficient Odd Odious Undulating Palindrome Palindromic Prime
How does the Number Property Calculator work?
This calculator determines if an integer you entered has any of the following properties:
* Even Numbers or Odd Numbers (Parity Function or even-odd numbers)
* Evil Numbers or Odious Numbers
* Perfect Numbers, Abundant Numbers, or Deficient Numbers
* Triangular Numbers
* Prime Numbers or Composite Numbers
* Automorphic (Curious)
* Undulating Numbers
* Square Numbers
* Cube Numbers
* Palindrome Numbers
* Repunit Numbers
* Apocalyptic Power
* Tetrahedral (Pyramidal)
* Narcissistic (Plus Perfect)
* Repunit This calculator has 1 input.
What 5 formulas are used for the Number Property Calculator?
Positive Numbers are greater than 0
Whole Numbers are positive numbers, including 0, with no decimal or fractional parts
Even numbers are divisible by 2
Odd Numbers are not divisible by 2
Palindromes have equal numbers when digits are reversed
What 11 concepts are covered in the Number Property Calculator?
a number by which another number is to be divided.
a given number base b is a number that is the sum of its own digits each raised to the power of the number of digits.
an arithmetical value, expressed by a word, symbol, or figure, representing a particular quantity and used in counting and making calculations and for showing order in a series or for identification. A quantity or amount.
A word or phrase which reads the same forwards or backwards
a polygon of five angles and five sides
A number that can be shown as a pentagonal pattern of dots. n(3n - 1)/2
a positive integer that is equal to the sum of its positive divisors, excluding the number itself.
an attribute, quality, or characteristic of something
Example calculations for the Number Property Calculator