A060299 - OEIS

%I #17 Jan 17 2023 15:33:33

%S 4,8,9,14,15,16,24,25,26,27,32,33,34,35,36,90,91,92,93,94,95,114,115,

%T 116,117,118,119,120,140,141,142,143,144,145,146,147,182,183,184,185,

%U 186,187,188,189,190,200,201,202,203,204,205,206,207,208,209,212,213

%N 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 Robert Israel, <a href="/A060299/b060299.txt">Table of n, a(n) for n = 1..10000</a>

%e Triangle starts:

%e    4;

%e    8,  9;

%e   14, 15, 16;

%e   24, 25, 26, 27;

%e   32, 33, 34, 35, 36;

%e   90, 91, 92, 93, 94, 95; - _Robert Israel_, Jan 17 2023

%e 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 R:= NULL: m:= 1;

%p p:= 3:

%p while m < 30 do

%p   q:= nextprime(p);

%p   g:= q-p-1;

%p   if g >= m then

%p     R:= R, $(p+1)..(p+m);

%p     p:= p+m;

%p     m:= m+1;

%p   else

%p     p:= q

%p   fi;

%p od:

%p R; # _Robert Israel_, Jan 17 2023

%Y First column gives A060064.

%K easy,nonn,tabl

%O 1,1

%A _Jason Earls_, Mar 25 2001

%E Name changed by _Robert Israel_, Jan 17 2023