The Mian–Chowla sequence is an integer sequence defined recursively.



Mian–Chowla is an infinite instance of a Sidon sequence, and belongs to the class known as B₂ sequences.



The sequence starts with:

a1 = 1
then for n > 1, an is the smallest positive integer such that every pairwise sum

ai + aj 
is distinct, for all i and j less than or equal to n.

The Task

 Find and display, here, on this page the first 30 terms of the Mian–Chowla sequence.
 Find and display, here, on this page the 91st through 100th terms of the Mian–Chowla sequence.


Demonstrating working through the first few terms longhand:

a1 = 1
1 + 1 = 2
Speculatively try a2 = 2

1 + 1 = 2
1 + 2 = 3
2 + 2 = 4
There are no repeated sums so 2 is the next number in the sequence.

Speculatively try a3 = 3

1 + 1 = 2
1 + 2 = 3 
1 + 3 = 4
2 + 2 = 4
2 + 3 = 5
3 + 3 = 6
Sum of 4 is repeated so 3 is rejected.

Speculatively try a3 = 4

1 + 1 = 2
1 + 2 = 3
1 + 4 = 5
2 + 2 = 4
2 + 4 = 6
4 + 4 = 8
There are no repeated sums so 4 is the next number in the sequence.

And so on...

See also

 OEIS:A005282 Mian-Chowla sequence
function mianchowla(n)
    seq = ones(Int, n)
    sums = Dict{Int,Int}()
    tempsums = Dict{Int,Int}()
    for i in 2:n
        seq[i] = seq[i - 1] + 1
        incrementing = true
        while incrementing
            for j in 1:i
                tsum = seq[j] + seq[i]
                if haskey(sums, tsum)
                    seq[i] += 1
                    empty!(tempsums)
                    break
                else
                    tempsums[tsum] = 0
                    if j == i
                        merge!(sums, tempsums)
                        empty!(tempsums)
                        incrementing = false
                    end
                end
            end
        end
    end
    seq
end
 
function testmianchowla()
    println("The first 30 terms of the Mian-Chowla sequence are $(mianchowla(30)).")
    println("The 91st through 100th terms of the Mian-Chowla sequence are $(mianchowla(100)[91:100]).")
end
 
testmianchowla()
@time testmianchowla()
 
 