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

1,1

Links

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

Example

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.

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

Crossrefs

First column gives A060064.

Sequence in context: A161757 A134376 A163408 * A120512 A046954 A112775

Adjacent sequences: A060296 A060297 A060298 * A060300 A060301 A060302

Keyword

easy,nonn,tabl

Author

Jason Earls, Mar 25 2001

Extensions

Name changed by Robert Israel, Jan 17 2023

Status

approved