OFFSET

1,3

COMMENTS

Conjecture:

- rows with indexes of the form 3*k converge to some sequence R:

R = 3, 5, 6, 10, 12, 15, 17, 19, 20, 21, 23, 24, 27, 29, 30, 33, 34, ...

- the other rows converge to some other sequence S:

S = 1, 2, 4, 7, 8, 9, 11, 13, 14, 16, 18, 22, 25, 26, 28, 31, 32, 36, ...

- R and S partition the positive integers,

- for any i, j, k:

R(i) <> S(j) * S(k),

S(i) <> R(k) * S(k).

LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..10011 (rows for n = 1..141 flattened)

EXAMPLE

Triangle T(n, k) begins:

1,

1, 2,

3, 4, 5,

1, 2, 7, 9,

1, 2, 7, 9, 11,

3, 5, 6, 8, 10, 12,

1, 2, 4, 7, 9, 11, 13,

1, 2, 4, 7, 9, 11, 13, 14,

3, 5, 6, 10, 12, 15, 17, 19, 20,

1, 2, 4, 7, 8, 9, 11, 13, 14, 16,

1, 2, 4, 7, 8, 9, 11, 13, 14, 16, 18,

3, 5, 6, 10, 12, 15, 17, 19, 20, 21, 23, 24,

...

PROG

(PARI) { rrr=rr=[]; for (n=1, 12, x=setbinop((i, j)->i*j, rrr, rr); r=vector(n); k=0; for (v=1, oo, if (!setsearch(x, v), print1 (r[k++]=v", "); if (k==n, break))); [rrr, rr]=[rr, r]) }

CROSSREFS

KEYWORD

nonn,tabl

AUTHOR

Rémy Sigrist, Jun 15 2022

STATUS

approved