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.

4, 8, 9, 14, 15, 16, 24, 25, 26, 27, 32, 33, 34, 35, 36, 90, 91, 92, 93, 94, 95, 114, 115, 116, 117, 118, 119, 120, 140, 141, 142, 143, 144, 145, 146, 147, 182, 183, 184, 185, 186, 187, 188, 189, 190, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 212, 213

Offset: 1

Author

Jason Earls, Mar 25 2001

Keywords

• easy
• nonn
• tabl

Examples

			Triangle starts:
   4;
   8,  9;
  14, 15, 16;
  24, 25, 26, 27;
  32, 33, 34, 35, 36;
  90, 91, 92, 93, 94, 95; - _Robert Israel_, Jan 17 2023
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.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

First column gives A060064.

Programs

Maple

R:= NULL: m:= 1;
p:= 3:
while m < 30 do
  q:= nextprime(p);
  g:= q-p-1;
  if g >= m then
    R:= R, $(p+1)..(p+m);
    p:= p+m;
    m:= m+1;
  else
    p:= q
  fi;
od:
R; # Robert Israel, Jan 17 2023

Extensions

Name changed by Robert Israel, Jan 17 2023