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
 
NB. http://rosettacode.org/wiki/Mian-Chowla_sequence
 
NB. Dreadfully inefficient implementation recomputes all the sums to n-1
NB. and computes the full addition table rather than just a triangular region
NB. However, this implementation is sufficiently quick to meet the requirements.
 
NB. The vector head is the next speculative value
NB. Beheaded, the vector is Mian-Chowla sequence.
 
 
Until =: conjunction def 'u^:(0 = v)^:_'
unique =: -:&# ~.   NB. tally of list matches that of set
 
next_mc =: [: (, {.) (>:@:{. , }.)Until(unique@:((<:/~@i.@# #&, +/~)@:(}. , {.)))
 
 
prime_q =: 1&p:   NB. for fun look at prime generation suitability
 