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A060299 Triangle T(m,n), 1 <= n <= m, read by rows: row m lists the first m consecutive composite numbers that are not in previous rows.

%I A060299 #17 Jan 17 2023 15:33:33
%S A060299 4,8,9,14,15,16,24,25,26,27,32,33,34,35,36,90,91,92,93,94,95,114,115,
%T A060299 116,117,118,119,120,140,141,142,143,144,145,146,147,182,183,184,185,
%U A060299 186,187,188,189,190,200,201,202,203,204,205,206,207,208,209,212,213
%N A060299 Triangle T(m,n), 1 <= n <= m, read by rows: row m lists the first m consecutive composite numbers that are not in previous rows.
%H A060299 Robert Israel, <a href="/A060299/b060299.txt">Table of n, a(n) for n = 1..10000</a>
%e A060299 Triangle starts:
%e A060299    4;
%e A060299    8,  9;
%e A060299   14, 15, 16;
%e A060299   24, 25, 26, 27;
%e A060299   32, 33, 34, 35, 36;
%e A060299   90, 91, 92, 93, 94, 95; - _Robert Israel_, Jan 17 2023
%e A060299 First occurrence of 1 consecutive composite gives 4, first occurrence of 2 consecutive composites gives 8 and 9, the first subsequent, disjoint occurrence of 3 consecutive composites gives 14, 15 and 16, etc.
%p A060299 R:= NULL: m:= 1;
%p A060299 p:= 3:
%p A060299 while m < 30 do
%p A060299   q:= nextprime(p);
%p A060299   g:= q-p-1;
%p A060299   if g >= m then
%p A060299     R:= R, $(p+1)..(p+m);
%p A060299     p:= p+m;
%p A060299     m:= m+1;
%p A060299   else
%p A060299     p:= q
%p A060299   fi;
%p A060299 od:
%p A060299 R; # _Robert Israel_, Jan 17 2023
%Y A060299 First column gives A060064.
%K A060299 easy,nonn,tabl
%O A060299 1,1
%A A060299 _Jason Earls_, Mar 25 2001
%E A060299 Name changed by _Robert Israel_, Jan 17 2023