%I
%S 1,8,9,4,12,21,14,18,30,51,6,20,38,68,119,10,16,36,74,142,261,22,32,
%T 48,84,158,300,561,27,49,81,129,213,371,671,1232,15,42,91,172,301,514,
%U 885,1556,2788,35,50,92,183,355,656,1170,2055,3611,6399,40,75,125,217,400,755,1411,2581,4636
%N Triangle read by antidiagonals: T[r+1,c] = T[r,c]+T[r,c+1], but only nonprime numbers may be used.
%C This sequence is the lexicographically earliest one satisfying the given constraint. It is built using the smallest possible choice for the next term [of the first row A203072] not leading to a contradiction.
%C Is this a permutation of the nonprimes?
%H Lars Blomberg, <a href="/A203071/b203071.txt">Table of n, a(n) for n = 1..20100 (the first 200 antidiagonals)</a>
%e row 1: 1 8 4 14 6 10 22 27 15 ... [A203072]
%e row 2: 9 12 18 20 16 32 49 42 ...
%e row 3: 21 30 38 36 48 81 91 ...
%e row 4: 51 68 74 84 129 172 ...
%e row 5: 119 142 158 213 301 ...
%e row 6: 261 300 371 514 ...
%e row 7: 561 671 885 ...
%e row 8: 1232 1556 ...
%e row 9: 2788 ...
%o (PARI) list_by_antidiagonals(a)={my(u=[]);for(i=1,#a,u=concat(u,a[i]);forstep(j=i1,1,1,u=concat(u,a[j]+=a[j+1])));u} /* requires the first line as input */
%K nonn,tabl
%O 1,2
%A _Eric Angelini_, Dec 28 2011
