Fifty seven (57)
1. It is a 20 gonal number.
2. It can be expressed as the sum of -- x^y + y^x where x and y are integers.
2^5 + 5^2 = 57
3. It is the sum of digits from 7 up to 12.
7 + 8 + 9 + 10 + 11 + 12 = 57
4. It is the product of two primes.
57 = 3 x 19
5. On base 7 it is a repeated digit.
57 = (111)7
Dr Rajesh Kumar Thakur
Monday, January 18, 2016
Mathematically 56
Fifty Six (56)
1. It is a tetrahedral number. It is the sum of first six triangular numbers.
1 + 3 + 6 + 10 + 15 + 21 = 56
2. It is an abundant number.
3. It is a tetranacci number. Like Fibonacci sequence, in the tetranacci numbers the next number is the sum of previous four terms. The first few tetranacci numbers are---
0, 0, 0, 1, 1, 2, 4, 8, 15, 29, 56, 108, 208, 401, 773—
4. It is the maximum number of regions into which 10 lines can divide a plane.
5. Here is an interesting puzzle involving 56.
111 + 1 / 1 + 1 = 56 222 + 2 / 2 + 2 = 56
333 + 3 / 3 + 3 = 56 444 + 4 / 4 + 4 = 56
6. The atomic number of Barium is 56.
7. The number of reduced 5 x 5 Latin square is 56. Here is an example---
1 2 3 4 5 2 3 5 1 4 3 5 4 2 1 4 1 2 5 3 5 4 1 3 2
Dr Rajesh Kumar Thakur
1. It is a tetrahedral number. It is the sum of first six triangular numbers.
1 + 3 + 6 + 10 + 15 + 21 = 56
2. It is an abundant number.
3. It is a tetranacci number. Like Fibonacci sequence, in the tetranacci numbers the next number is the sum of previous four terms. The first few tetranacci numbers are---
0, 0, 0, 1, 1, 2, 4, 8, 15, 29, 56, 108, 208, 401, 773—
4. It is the maximum number of regions into which 10 lines can divide a plane.
5. Here is an interesting puzzle involving 56.
111 + 1 / 1 + 1 = 56 222 + 2 / 2 + 2 = 56
333 + 3 / 3 + 3 = 56 444 + 4 / 4 + 4 = 56
6. The atomic number of Barium is 56.
7. The number of reduced 5 x 5 Latin square is 56. Here is an example---
1 2 3 4 5 2 3 5 1 4 3 5 4 2 1 4 1 2 5 3 5 4 1 3 2
Dr Rajesh Kumar Thakur
Mathematically 55
Fifty Five (55)
1. It is the sum of first 10 natural numbers.
1 + 2 + --+10 = 55
2. It is a triangular number. It is the first triangular number composed of repeated digits.
The other are 66 and 666.
3. It is the largest triangular number in Fibonacci sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, 55…
4. The sum of squares of first five natural numbers is 55. The sum of squares of n natural number is given by --- 1^2 + 2^2 + 3^2 +---- + n^2 = n (n+1) (2n+1) /6
1^2 + 2^2 + 3^2 + 4^2 + 5^2 = 55
5. It is a Palindromic number.
6. Every integer greater than 55 is the sum of distinct primes of the form 4n + 3.
7. The square of 55 shows an interesting pattern.
55^2 = 3025 and 30 + 25 = 55
8. It is the product of 3rd and 5th prime numbers.
55 = 5 x 11
9. Sum of 8 factors of 36 is 55.
1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 = 55
10. It is a square pyramidal number.
11. It is a centered nonagonal number.
12. It is a centered 18 - gonal number.
13. It is the 4th Kaprekar number.
14. It is a cubic recurring digital invariant. Add the cubes of its digits together and repeat the operation twice and you will get 55 back.
55 : 5^3 + 5^3 = 250
250: 2^3 + 5^3 + 0^3 = 133
133: 1^3 + 3^3 + 3^3 = 55
15. It is a heptagonal number. A polygonal number of the form of n(5n – 3 ) / 2 is called heptagonal number.
16. If you multiply any odd numbers from 91 to 109 by 55, you will get a palindrome number each time.
91 x 55 = 5005 93 x 55 = 5115
17. We all know
3^2 + 4 ^2 = 5^2
but 33^2 + 44^2 = 55^2
Dr Rajesh Kumar Thakur
1. It is the sum of first 10 natural numbers.
1 + 2 + --+10 = 55
2. It is a triangular number. It is the first triangular number composed of repeated digits.
The other are 66 and 666.
3. It is the largest triangular number in Fibonacci sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, 55…
4. The sum of squares of first five natural numbers is 55. The sum of squares of n natural number is given by --- 1^2 + 2^2 + 3^2 +---- + n^2 = n (n+1) (2n+1) /6
1^2 + 2^2 + 3^2 + 4^2 + 5^2 = 55
5. It is a Palindromic number.
6. Every integer greater than 55 is the sum of distinct primes of the form 4n + 3.
7. The square of 55 shows an interesting pattern.
55^2 = 3025 and 30 + 25 = 55
8. It is the product of 3rd and 5th prime numbers.
55 = 5 x 11
9. Sum of 8 factors of 36 is 55.
1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 = 55
10. It is a square pyramidal number.
11. It is a centered nonagonal number.
12. It is a centered 18 - gonal number.
13. It is the 4th Kaprekar number.
14. It is a cubic recurring digital invariant. Add the cubes of its digits together and repeat the operation twice and you will get 55 back.
55 : 5^3 + 5^3 = 250
250: 2^3 + 5^3 + 0^3 = 133
133: 1^3 + 3^3 + 3^3 = 55
15. It is a heptagonal number. A polygonal number of the form of n(5n – 3 ) / 2 is called heptagonal number.
16. If you multiply any odd numbers from 91 to 109 by 55, you will get a palindrome number each time.
91 x 55 = 5005 93 x 55 = 5115
17. We all know
3^2 + 4 ^2 = 5^2
but 33^2 + 44^2 = 55^2
Dr Rajesh Kumar Thakur
Mathematically 54
Fifty Four (54)
1. It is an abundant number.
2. It is the smallest number that can be written as the sum of 3 squares in 3 different ways.
54 = 7^2 + 1^2 + 2^2 = 6^2 + 3^2 + 3^2 = 5^2 + 5^2 + 2^2
3. It is the sum of first 9 natural numbers starting from 2.
2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 54
4. There are 54 coloured squares on a standard Rubik’s cube. Each of 6 faces has 9 squares. This was invented by Hungarian Sculptor Erno Rubik in 1974.
5. It is a Leyland number. A Leyland number is written in the form of x^y + y^x where x and y are integers greater than 1. The first few Leyland numbers are --- 8, 17, 32, 54, 57---
6. The atomic number of Xenon is 54.
7. It is a Harshad number because it is divisible by the sum of its digits.
8. It is a 19- gonal number.
Dr Rajesh Kumar Thakur
1. It is an abundant number.
2. It is the smallest number that can be written as the sum of 3 squares in 3 different ways.
54 = 7^2 + 1^2 + 2^2 = 6^2 + 3^2 + 3^2 = 5^2 + 5^2 + 2^2
3. It is the sum of first 9 natural numbers starting from 2.
2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 54
4. There are 54 coloured squares on a standard Rubik’s cube. Each of 6 faces has 9 squares. This was invented by Hungarian Sculptor Erno Rubik in 1974.
5. It is a Leyland number. A Leyland number is written in the form of x^y + y^x where x and y are integers greater than 1. The first few Leyland numbers are --- 8, 17, 32, 54, 57---
6. The atomic number of Xenon is 54.
7. It is a Harshad number because it is divisible by the sum of its digits.
8. It is a 19- gonal number.
Dr Rajesh Kumar Thakur
Mathematically 53
Fifty Three (53)
1. It is a Prime number.
2. If there are 53 people in a room it is very likely that at least two of them share the same birthday.
3. It is the only two digit number which on reverse changes into a hexadecimal base.
53 = 3516
4. The sum of all consecutive primes from 7 to 53 is the product of 7 and 53.
7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37+ 41+ 43 + 47 + 53 = 371 = 7 x 53
5. It can be expressed as the sum of squares in two different ways.
53 = 22 + 72 = 12 + 42 + 62
6. The sum of 53 prime numbers is divisible by 53.
2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97 + 101 + 103 + 107 + 109 + 113 + 127 + 131 + 137 + 139 + 149 + 151 + 157 + 163 + 173 + 179 + 181 + 191 + 197 + 199 + 211 + 223 + 227 + 229 + 547 = 5830 = 53 x 110
7. The sum of first 53 natural numbers is also divisible by 53.
1 + 2 + 3---- + 53 = 1431 = 53 x 27
8. It is the sum of five consecutive primes starting from 5.
5 + 7 + 11 + 13 + 17 = 53
9. It is the smallest prime which is not the difference between powers of 2 and 3.
10. Atomic number of Iodine is 53.
Dr Rajesh Kumar Thakur
rkthakur1974@gmail.com
1. It is a Prime number.
2. If there are 53 people in a room it is very likely that at least two of them share the same birthday.
3. It is the only two digit number which on reverse changes into a hexadecimal base.
53 = 3516
4. The sum of all consecutive primes from 7 to 53 is the product of 7 and 53.
7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37+ 41+ 43 + 47 + 53 = 371 = 7 x 53
5. It can be expressed as the sum of squares in two different ways.
53 = 22 + 72 = 12 + 42 + 62
6. The sum of 53 prime numbers is divisible by 53.
2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97 + 101 + 103 + 107 + 109 + 113 + 127 + 131 + 137 + 139 + 149 + 151 + 157 + 163 + 173 + 179 + 181 + 191 + 197 + 199 + 211 + 223 + 227 + 229 + 547 = 5830 = 53 x 110
7. The sum of first 53 natural numbers is also divisible by 53.
1 + 2 + 3---- + 53 = 1431 = 53 x 27
8. It is the sum of five consecutive primes starting from 5.
5 + 7 + 11 + 13 + 17 = 53
9. It is the smallest prime which is not the difference between powers of 2 and 3.
10. Atomic number of Iodine is 53.
Dr Rajesh Kumar Thakur
rkthakur1974@gmail.com
Mathematically 52
Fifty Two (52)
1. The number of playing cards is 52. It contains 4 suits (Heart, Diamond, Clubs, and Spades) each of 13 in numbers. The 52 cards have 26 Black and 26 Red Cards. 4 kings, 4 queens, and 4 ace are known as ace cards.
2. It is the sum of two consecutive primes.
52 = 23 + 29
3. A piano has 52 white keys.
4. It is the sum of 6 Fibonacci number starting from the 3rd.
52 = 2 + 3 + 5 + 8 + 13 + 21
5. A year has 52 weeks.
6. It is a 6th Bell number. Bell numbers are named after the mathematician Eric Temple Bell. It is the number of partitions of a set with n members or the number of equivalence relation on it. The first 6 Bell numbers are –
1, 1, 2, 5, 15, 52---
The Bell numbers can be generated by the following table, which works kind of like Pascal's Triangle.
7. It is a decagonal number.
8. It is a 3rd Untouchable number. An untouchable number is a positive integer that can’t be expressed as the sum of all the proper divisors of any positive integer including the untouchable number itself. The first few untouchable numbers are 2, 5, 52, 88---
9. The atomic number of Tellurium is 52.
Dr Rajesh Kumar Thakur
1. The number of playing cards is 52. It contains 4 suits (Heart, Diamond, Clubs, and Spades) each of 13 in numbers. The 52 cards have 26 Black and 26 Red Cards. 4 kings, 4 queens, and 4 ace are known as ace cards.
2. It is the sum of two consecutive primes.
52 = 23 + 29
3. A piano has 52 white keys.
4. It is the sum of 6 Fibonacci number starting from the 3rd.
52 = 2 + 3 + 5 + 8 + 13 + 21
5. A year has 52 weeks.
6. It is a 6th Bell number. Bell numbers are named after the mathematician Eric Temple Bell. It is the number of partitions of a set with n members or the number of equivalence relation on it. The first 6 Bell numbers are –
1, 1, 2, 5, 15, 52---
The Bell numbers can be generated by the following table, which works kind of like Pascal's Triangle.
7. It is a decagonal number.
8. It is a 3rd Untouchable number. An untouchable number is a positive integer that can’t be expressed as the sum of all the proper divisors of any positive integer including the untouchable number itself. The first few untouchable numbers are 2, 5, 52, 88---
9. The atomic number of Tellurium is 52.
Dr Rajesh Kumar Thakur
Mathematically 51
Fifty One (51)
1. It is a Pentagonal number as well as Centered Pentagonal number.
2. It is the smallest number which can be written with the digits 1 to 5 as the sum of prime numbers. 51 = 2 + 3 + 5 + 41
3. It is the sum of 6 numbers in an AP with common difference 3.
51 = 1 + 4 + 7 + 10 + 13 + 16
4. It is equal to sum of 6 numbers from 6 to 11.
51 = 6 + 7 + 8 + 9 + 10 + 11
5. It is a 18- gonal number.
6. It is the product of two primes.
51 = 3 x 17
7. It is a 6th Motzkin number. For a given number n, Motzkin number is the number of different ways of drawing chords on a circle between n points. It is named after Theodore Motzkin. The first few Motzin numbers are- 1, 2, 4, 9, 21, 51-----
8. The atomic number of Antimony is 71,
Dr Rajesh Kumar Thakur
1. It is a Pentagonal number as well as Centered Pentagonal number.
2. It is the smallest number which can be written with the digits 1 to 5 as the sum of prime numbers. 51 = 2 + 3 + 5 + 41
3. It is the sum of 6 numbers in an AP with common difference 3.
51 = 1 + 4 + 7 + 10 + 13 + 16
4. It is equal to sum of 6 numbers from 6 to 11.
51 = 6 + 7 + 8 + 9 + 10 + 11
5. It is a 18- gonal number.
6. It is the product of two primes.
51 = 3 x 17
7. It is a 6th Motzkin number. For a given number n, Motzkin number is the number of different ways of drawing chords on a circle between n points. It is named after Theodore Motzkin. The first few Motzin numbers are- 1, 2, 4, 9, 21, 51-----
8. The atomic number of Antimony is 71,
Dr Rajesh Kumar Thakur
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