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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.
2
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
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
KEYWORD
easy,nonn,tabl
AUTHOR
Jason Earls, Mar 25 2001
EXTENSIONS
Name changed by Robert Israel, Jan 17 2023
STATUS
approved