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
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
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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