The Purpose of creating the page is to inspire the young brainsto search and think about interesting properties of special numbers

Important: Interesting numbers are the one which possess some special characteristic. Such as Ramanujan number 1729, as it can be uniquely written as sum of the cubes of two positive numbers. The students shall find special numbers keeping this aspect in mind. The numbers should not be taken on the basis of the group to which they belong like a natural number, or complex numbers.

INTER SCHOOL WORKSHOP ON CURIOUS AND INTERESTING NUMBER

A workshop on what we mean by curious and interesting numbers. Workshop being conducted by Mr Ajay Marwaha.

Ashwin IX-D I have found, their are triangular numbers, which can be defined as :--

A triangular number or triangle number counts the objects that can form an equilateral triangle, as in the
adjoining figure done by me

Comment: Ashwin Give some examples

Pradeep X-B

THE NUMBER : WOODALL NUMBER:

Natural number of the form Wn = n . 2n - 1 , where n is a natural number is known as Woodall number

Examples: 1, 7, 23, 63, 159, 383, 895

The numbers were first studied by Allan J.C. Cunningham and H.J. Woodall in 1917
Comment: Good job, try finding application if any

KASHISH - XI A2

THE NUMBER: SCHRODER NUMBER

Definition- Schroder number describes the number of paths from the southwest corner (0,0) of an n x n grid to the northeast corner(n,n), using only single steps north, northeast, or east, that do not rise above the SW-NE diagonal.

Examples- 1, 2, 6, 22, 90, 394, 1806, 8558….

History- Ernst Schroder in 19th century.

Origin- Germany

Comment: Kashish can we elaborate a little.

SURESH- XD

Comment: where is 6th taxi cab number

Sir, Here is the 6th taxi cab number
Comment: Good

RAJAT:XI-B1

THE NUMBER: VAMPIRE NUMBER A Vampire Number is a composite natural number v, with an even number of digits n, that can be factored into two integers x and y each with n/2 digits and not both with trailing zeroes, where v contains precisely all the digits form x and from y, in order, counting multiplicity. x and y are called the fangs.
EXAMPLE: 1260 is a vampire number with 21 and 60 as fangs since 21 x 60 = 1260 . Some more vampire numbers are 1395, 1435, 1530, 1827 etc

PARUL X-B

THE NUMBER: UNDULANT NUMBER

An undulant number is a number where its digits go up and down like the numbers 461902 or 708143 or even 1010101, but not 123 because 2 < 3.

SMRITI - IX-A

THE NUMBER: THABIT NUMBER

A Thabit number is an integer of the form 3 . 2^n - 1 for a non-negative integer n.

The numbers are named after Thabit ibn Qurra who was born in Harran in 210-211 A.H./ 826 A.D.

Comment: Good

RASHMI- IX-C

THE NUMBER: PYTHAGOREAN NUMBER
The Pythagorean number is area of the triangle whose sides are Pythagorean triplet’s i.e. if a^2 + b^2 = c^2 , where a, b and c are natural numbers then the area of triangle is (1/2 a.b) which is the Pythagorean number.

EXAMPLE: As 3^2 + 4^2 = 5^2 thus the Pythagorean number is 1/2 . 3.4 = 6, other examples of Pythagorean number are 24, 30, 54, 60, 84, 96, 120, 150 etc.

The numbers are defined by famous mathematician Pythagoras.

Comment: Good

DEEPANSHU JINDAL - XI A2.

THE NUMBER: n-PERSISTENT NUMBER

An n-Persistent Number is a positive integer ‘k’ which contains the digits 0, 1, 2, 3, … , 9 and for which 2k, …. , nk also share this property.

EXAMPLE: k = 1234567890 is 2-persistent number, since 2k = 2469135780 but 3k = 3703703670

VARUN VERMA - IX-C

THE NUMBER: FRIEDMAN NUMBER

A Friedman number is a positive integer which can be written in some non-trivial way using its own digits,
together with the symbols +,−, ×,÷ or exponents

E.g. 25 = 5^2 and 126 = 21 × 6. Some Friedman number are 25, 121, 125,126,127, 128, 153, 216, 289, 343, 347, 625, 688, 736, 1022, 1024.

SANJAY - X-C

THE NUMBER: MERSENNE NUMBER

A prime number of the number Mn = 2^n - 1, where n is an integer is known as a Mersenne number.

E.g. for n = 3, 7 = 2^3 - 1. The first few Mersenne numbers are 1, 3, 7, 15, 31, 63, 127, 255.

SHRUTI-XI-A2

THE NUMBER: PROTH NUMBER

In number theory, a Proth number, named after the mathematician François Proth, is a number of the form N = k x 2^n + 1 where k is an odd number, n is a positive integer, and 2^n > k.

EXAMPLE: The first few Proth numbers are 3,5,9,13,17,25,33,41,49,57,65.

ASHISH - IX - A

SOME NUMBERS AND THEIR CATEGORIES

0 - is the additive identity. 1- is the multiplicative identity. 2 - is the only even prime. 3 - is the number of spatial dimensions we live in. 4 - is the smallest number of colors sufficient to color all planar maps. 5 - is the number of Platonic solids. 6 - is the smallest perfect number. 7 - is the smallest number of sides of a regular polygon that is not constructible by
straightedge and compass.

8 - is the largest cube in the Fibonacci sequence.

9 - is the maximum number of cubes that are needed to sum to any positive integer. 10 - is the base of our number system. 11 - is the largest known multiplicative persistence. 12 - is the smallest abundant number. 13 - is the number of Archimedian solids. 14 - is the smallest even number n with no solutions to φ(m) = n. 15 - is the smallest composite number n with the property that there is only one group of order n.

16 - is the only number of the form xy = yx with x and y being different integers.

The Purpose of creating the page is to inspire the young brainsto search and think about interesting properties of special numbersImportant:Interesting numbers are the one which possess some special characteristic. Such as Ramanujan number 1729, as it can be uniquely written as sum of the cubes of two positive numbers. The students shall find special numbers keeping this aspect in mind. The numbers should not be taken on the basis of the group to which they belong like a natural number, or complex numbers.INTER SCHOOL WORKSHOP ON CURIOUS AND INTERESTING NUMBER

A workshop on what we mean by curious and interesting numbers. Workshop being conducted by Mr Ajay Marwaha.

Ashwin IX-DI have found, their are triangular numbers, which can be defined as :--A

triangular numberortriangle numbercounts the objects that can form an equilateral triangle, as in theadjoining figure done by me

Comment: Ashwin Give some examples

Pradeep X-B

THE NUMBER : WOODALL NUMBER:

Natural number of the form Wn = n . 2n - 1 , where n is a natural number is known as Woodall number

Comment: Good job, try finding application if any

KASHISH - XI A2

THE NUMBER: SCHRODER NUMBER

Definition-Schroder number describes the number of paths from the southwest corner (0,0) of an n x n grid to the northeast corner(n,n), using only single steps north, northeast, or east, that do not rise above the SW-NE diagonal.Examples-1, 2, 6, 22, 90, 394, 1806, 8558….History-Ernst Schroder in 19th century.Origin-GermanyComment: Kashish can we elaborate a little.

SURESH- XD

Comment: where is 6th taxi cab number

Sir, Here is the 6th taxi cab number

Comment: Good

RAJAT:XI-B1

THE NUMBER: VAMPIRE NUMBER

A Vampire Number is a composite natural number v, with an even number of digits n, that can be factored into two integers x and y each with n/2 digits and not both with trailing zeroes, where v contains precisely all the digits form x and from y, in order, counting multiplicity. x and y are called the fangs.

EXAMPLE: 1260 is a vampire number with 21 and 60 as fangs since 21 x 60 = 1260 . Some more vampire numbers are 1395, 1435, 1530, 1827 etc

PARUL X-B

THE NUMBER: UNDULANT NUMBER

An undulant number is a number where its digits go up and down like the numbers 461902 or 708143 or even 1010101, but not 123 because 2 < 3.

SMRITI - IX-A

THE NUMBER: THABIT NUMBER

A Thabit number is an integer of the form 3 . 2^n - 1 for a non-negative integer n.

Examples: 2, 5, 11, 23, 47, 95, 191, 383, 767, 1535 etc.

The numbers are named after Thabit ibn Qurra who was born in Harran in 210-211 A.H./ 826 A.D.

Comment: Good

RASHMI- IX-C

THE NUMBER: PYTHAGOREAN NUMBER

The Pythagorean number is area of the triangle whose sides are Pythagorean triplet’s i.e. if a^2 + b^2 = c^2 , where a, b and c are natural numbers then the area of triangle is (1/2 a.b) which is the Pythagorean number.

EXAMPLE: As 3^2 + 4^2 = 5^2 thus the Pythagorean number is 1/2 . 3.4 = 6, other examples of Pythagorean number are 24, 30, 54, 60, 84, 96, 120, 150 etc.

The numbers are defined by famous mathematician Pythagoras.

Comment: Good

DEEPANSHU JINDAL - XI A2.

THE NUMBER: n-PERSISTENT NUMBER

An n-Persistent Number is a positive integer ‘k’ which contains the digits 0, 1, 2, 3, … , 9 and for which 2k, …. , nk also share this property.

EXAMPLE: k = 1234567890 is 2-persistent number, since 2k = 2469135780 but 3k = 3703703670

VARUN VERMA - IX-C

THE NUMBER: FRIEDMAN NUMBER

A Friedman number is a positive integer which can be written in some non-trivial way using its own digits,

together with the symbols +,−, ×,÷ or exponents

E.g. 25 = 5^2 and 126 = 21 × 6. Some Friedman number are 25, 121, 125,126,127, 128, 153, 216, 289, 343, 347, 625, 688, 736, 1022, 1024.

SANJAY - X-C

THE NUMBER: MERSENNE NUMBER

A prime number of the number Mn = 2^n - 1, where n is an integer is known as a Mersenne number.

E.g. for n = 3, 7 = 2^3 - 1. The first few Mersenne numbers are 1, 3, 7, 15, 31, 63, 127, 255.

SHRUTI-XI-A2

THE NUMBER: PROTH NUMBER

In number theory, a Proth number, named after the mathematician François Proth, is a number of the form N = k x 2^n + 1 where k is an odd number, n is a positive integer, and 2^n > k.

EXAMPLE: The first few Proth numbers are 3,5,9,13,17,25,33,41,49,57,65.

ASHISH - IX - A

SOME NUMBERS AND THEIR CATEGORIES

0 - is the additive identity.

1- is the multiplicative identity.

2 - is the only even prime.

3 - is the number of spatial dimensions we live in.

4 - is the smallest number of colors sufficient to color all planar maps.

5 - is the number of Platonic solids.

6 - is the smallest perfect number.

7 - is the smallest number of sides of a regular polygon that is not constructible by

straightedge and compass.

## 8 - is the largest cube in the Fibonacci sequence.

9 - is the maximum number of cubes that are needed to sum to any positive integer.10 - is the base of our number system.

11 - is the largest known multiplicative persistence.

12 - is the smallest abundant number.

13 - is the number of Archimedian solids.

14 - is the smallest even number n with no solutions to φ(m) = n.

15 - is the smallest composite number n with the property that there is only one group of order n.

16 - is the only number of the form xy = yx with x and y being different integers.