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
  [ stack ]                          is makeable    (   --> s )
 
  [ temp put
    1 bit makeable put
    ' [ 1 ] 1
    [ true temp put
      1+
      over witheach
        [ over + bit
          makeable share & if
            [ false temp replace
              conclude ] ]
      temp take if
        [ dup dip join 
          over witheach
           [ over + bit
             makeable take
             | makeable put ] ]
      over size temp share = until ]
    makeable release
    temp release
    drop ]                           is mian-chowla ( n --> [ )
 
100 mian-chowla
30 split swap echo cr
-10 split nip echo