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.

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

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

Index entries for sequences that are permutations of the natural numbers

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

Adjacent sequences: A360368 A360369 A360370 * A360372 A360373 A360374

Keyword

nonn,tabl

Author

Samuel Harkness, Mar 17 2023

Status

approved