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A360371
Triangle read by rows: lexicographically earliest sequence of distinct positive integers such that each column contains only multiples of the first number in that column. See example.
3
1, 2, 3, 4, 6, 5, 7, 9, 10, 8, 11, 12, 15, 16, 13, 14, 18, 20, 24, 26, 17, 19, 21, 25, 32, 39, 34, 22, 23, 27, 30, 40, 52, 51, 44, 28, 29, 33, 35, 48, 65, 68, 66, 56, 31, 36, 42, 45, 64, 78, 85, 88, 84, 62, 37, 38, 54, 50, 72, 91, 102, 110, 112, 93, 74, 41
OFFSET
1,2
COMMENTS
A permutation of the natural numbers.
Among the first number of columns, are there more primes or composites? Of the first 500 columns, 296 are prime, 203 are composite (first column begins with 1).
LINKS
EXAMPLE
The start of the sequence as a triangular array read by rows:
1;
2, 3;
4, 6, 5;
7, 9, 10, 8;
11, 12, 15, 16, 13;
14, 18, 20, 24, 26, 17;
19, 21, 25, 32, 39, 34, 22;
23, 27, 30, 40, 52, 51, 44, 28;
...
Note that each column contains only multiples of the first number in the column.
For a(17), note that we are in the second column, so a(17) must be a positive multiple of 3. No numbers can be repeated, and we see that {3, 6, 9, 12, 15} have already been used, and 18 is the smallest unused positive multiple of 3. Therefore, a(17) = 18.
MAPLE
b:= proc() false end:
T:= proc(n, k) option remember; local j;
if {n, k} = {1} then j:=1
elif n=k then for j from T(n-1$2) while b(j) do od
else for j from T(n-1, k) by T(k, k) while b(j) do od
fi; b(j):=true; j
end:
seq(seq(T(n, k), k=1..n), n=1..12); # Alois P. Heinz, Mar 19 2023
PROG
(MATLAB) See Links section.
CROSSREFS
Cf. A194982, A361251 (inverse).
Sequence in context: A342798 A132284 A131966 * A194970 A194982 A064578
KEYWORD
nonn,tabl
AUTHOR
Samuel Harkness, Mar 17 2023
STATUS
approved