A289281 Square array whose rows m >= 2 hold the limit under iterations of the morphism { x -> (x, ..., x+k-1) if k|x ; x -> x+1 otherwise }, starting with (0); read by falling antidiagonals.

0, 1, 0, 2, 1, 0, 2, 2, 1, 0, 3, 2, 2, 1, 0, 2, 3, 3, 2, 1, 0, 3, 3, 2, 3, 2, 1, 0, 4, 3, 3, 4, 3, 2, 1, 0, 2, 4, 4, 2, 4, 3, 2, 1, 0, 3, 5, 3, 3, 5, 4, 3, 2, 1, 0, 4, 3, 4, 4, 2, 5, 4, 3, 2, 1, 0, 4, 4, 4, 5, 3, 6, 5, 4, 3, 2, 1, 0, 5, 5, 5, 3, 4, 2, 6, 5, 4, 3, 2, 1, 0, 2, 3, 6, 4, 5, 3, 7, 6, 5, 4, 3, 2, 1, 0, 3, 4, 7, 5, 6, 4, 2, 7, 6, 5, 4, 3, 2, 1, 0, 4, 5, 4, 5, 3, 5, 3, 8, 7, 6, 5, 4

Offset

2,4

Comments

The generalization of A104234 (row 2) and A288577 (row 3) to arbitrary m.

Links

Kerry Mitchell, Table of n, a(n) for n = 2..10012

Example

The array starts (first row: m=2)
  [ 0 1 2 2 3 2 3 4 2 3  4  4  5  2  3  4  4  5  4  5  6  2  3  4  4 ...]
  [ 0 1 2 2 3 3 3 4 5 3  4  5  3  4  5  5  6  3  4  5  5  6  3  4  5 ...]
  [ 0 1 2 3 2 3 4 3 4 4  5  6  7  4  4  5  6  7  4  5  6  7  6  7  8 ...]
  [ 0 1 2 3 4 2 3 4 5 3  4  5  5  6  7  8  9  4  5  5  6  7  8  9  5 ...]
  [ 0 1 2 3 4 5 2 3 4 5  6  3  4  5  6  6  7  8  9 10 11  4  5  6  6 ...]
  [ 0 1 2 3 4 5 6 2 3 4  5  6  7  3  4  5  6  7  7  8  9 10 11 12 13 ...]
  [ 0 1 2 3 4 5 6 7 2 3  4  5  6  7  8  3  4  5  6  7  8  8  9 10 11 ...]
  [ 0 1 2 3 4 5 6 7 8 2  3  4  5  6  7  8  9  3  4  5  6  7  8  9  9 ...]
  [ 0 1 2 3 4 5 6 7 8 9  2  3  4  5  6  7  8  9 10  3  4  5  6  7  8 ...]
  [ 0 1 2 3 4 5 6 7 8 9 10  2  3  4  5  6  7  8  9 10 11  3  4  5  6 ...]
  [ 0 1 2 3 4 5 6 7 8 9 10 11  2  3  4  5  6  7  8  9 10 11 12  3  4 ...]
  [ 0 1 2 3 4 5 6 7 8 9 10 11 12  2  3  4  5  6  7  8  9 10 11 12 13 ...]
  ...
It is easy to prove that row m starts with (0, ..., m-1; 2, ..., m; 3, ..., m; m, ..., 2m-1; ...).

Prog

(PARI) A289281_row(n=30, k=2, a=[0])={while(#a<n, a=concat(vector(#a, j, if(a[j]%k, a[j]+1, vector(k, i, a[j]+i-1))))); a}

Crossrefs

Cf. A104234 (row 2), A288577 (row 3).

Sequence in context: A045832 A287528 A328312 * A374996 A212957 A035393

Adjacent sequences: A289278 A289279 A289280 * A289282 A289283 A289284

Keyword

nonn,tabl

Author

M. F. Hasler, Jul 01 2017

Status

approved