mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

, the Mian–Chowla sequence is an integer sequence defined recursively in the following way. The sequence starts with :

a_1 = 1.

Then for

n>1

a_n

is the smallest integer such that every pairwise sum :

a_i + a_j

is distinct, for all

i

and

j

less than or equal to

n

Properties

Initially, with

a_1

, there is only one pairwise sum, 1 + 1 = 2. The next term in the sequence,

a_2

, is 2 since the pairwise sums then are 2, 3 and 4, i.e., they are distinct. Then,

a_3

can't be 3 because there would be the non-distinct pairwise sums 1 + 3 = 2 + 2 = 4. We find then that

a_3 = 4

, with the pairwise sums being 2, 3, 4, 5, 6 and 8. The sequence thus begins : 1, 2, 4, 8, 13, 21, 31, 45, 66, 81, 97,

123 123 may refer to: * The first three positive Arabic numerals * 123 (number), the natural number following 122 and preceding 124 * AD 123, a year of the Julian calendar, in the second century AD * 123 BC, a year of the pre-Julian Roman calendar En ...

148 148 may refer to: *148 (number), a natural number *AD 148, a year in the 2nd century AD *148 BC, a year in the 2nd century BC *148 (album), an album by C418 *148 (Meiktila) Battery Royal Artillery *148 (New Jersey bus) 148 may refer to: *148 (numb ...

182 Year 182 ( CLXXXII) was a common year starting on Monday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Sura and Rufus (or, less frequently, year 935 ''Ab urbe condita'') ...

204 __NOTOC__ Year 204 (CCIV) was a leap year starting on Sunday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Cilo and Flavius (or, less frequently, year 957 ''Ab urbe co ...

, 252,

290 __NOTOC__ Year 290 ( CCXC) was a common year starting on Wednesday (link will display the full calendar) of the Julian calendar. In the Roman Empire, it was known as the Year of the Consulship of Valerius and Valerius (or, less frequently, ye ...

, 361, 401, 475, ... .

Similar sequences

If we define

a_1 = 0

, the resulting sequence is the same except each term is one less (that is, 0, 1, 3, 7, 12, 20, 30, 44, 65, 80, 96, ... ).

History

The sequence was invented by Abdul Majid Mian and

Sarvadaman Chowla Sarvadaman D. S. Chowla (22 October 1907 – 10 December 1995) was an Indian American mathematician, specializing in number theory. Early life He was born in London, since his father, Gopal Chowla, a professor of mathematics in Lahore, was then s ...

References

* S. R. Finch, ''Mathematical Constants'', Cambridge (2003): Section 2.20.2 * R. K. Guy ''Unsolved Problems in Number Theory'', New York: Springer (2003) {{DEFAULTSORT:Mian-Chowla sequence Integer sequences