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
Rémy Sigrist, Table of n, a(n) for n = 1..10011 (first 141 rows flattened)
Samuel Harkness, First 500000 terms
Samuel Harkness, MATLAB program
Rémy Sigrist, PARI program
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
KEYWORD
nonn,tabl
AUTHOR
Samuel Harkness, Mar 17 2023
STATUS
approved