A348043 Square array A(n,k) = the nearest common ancestor of n and n*k in Doudna tree (A005940).

1, 1, 2, 1, 2, 3, 1, 2, 3, 4, 1, 2, 2, 4, 5, 1, 2, 3, 2, 5, 6, 1, 2, 3, 4, 3, 6, 7, 1, 2, 2, 2, 5, 2, 7, 8, 1, 2, 3, 2, 2, 6, 5, 8, 9, 1, 2, 3, 2, 3, 6, 7, 2, 9, 10, 1, 2, 2, 4, 3, 2, 3, 8, 4, 10, 11, 1, 2, 3, 4, 5, 3, 5, 2, 9, 3, 11, 12, 1, 2, 3, 2, 3, 6, 2, 2, 2, 10, 7, 12, 13, 1, 2, 2, 2, 2, 2, 7, 2, 4, 2, 11, 2, 13, 14

Offset

1,3

Comments

Array is read by falling antidiagonals as A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), ...

Links

Table of n, a(n) for n=1..105.

Index entries for sequences computed from indices in prime factorization

Formula

A(n, k) = A348041(n, n*k).

Example

The top left 17x17 corner of the array:
  n/k |   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16  17
------+----------------------------------------------------------------------
    1 |   1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1,
    2 |   2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,  2,
    3 |   3,  3,  2,  3,  3,  2,  3,  3,  2,  3,  3,  2,  3,  3,  3,  3,  3,
    4 |   4,  4,  2,  4,  2,  2,  2,  4,  4,  2,  2,  2,  2,  2,  2,  4,  2,
    5 |   5,  5,  3,  5,  2,  3,  3,  5,  3,  2,  5,  3,  5,  3,  2,  5,  5,
    6 |   6,  6,  2,  6,  6,  2,  3,  6,  2,  6,  3,  2,  3,  3,  6,  6,  3,
    7 |   7,  7,  5,  7,  3,  5,  2,  7,  5,  3,  3,  5,  5,  2,  3,  7,  7,
    8 |   8,  8,  2,  8,  2,  2,  2,  8,  4,  2,  2,  2,  2,  2,  2,  8,  2,
    9 |   9,  9,  4,  9,  2,  4,  2,  9,  4,  2,  2,  4,  2,  2,  2,  9,  2,
   10 |  10, 10,  3, 10,  2,  3,  3, 10,  3,  2, 10,  3,  5,  3,  2, 10,  5,
   11 |  11, 11,  7, 11,  5,  7,  3, 11,  7,  5,  2,  7,  3,  3,  5, 11,  5,
   12 |  12, 12,  2, 12,  6,  2,  3, 12,  2,  6,  3,  2,  3,  3, 12, 12,  3,
   13 |  13, 13, 11, 13,  7, 11,  5, 13, 11,  7,  3, 11,  2,  5,  7, 13,  3,
   14 |  14, 14,  5, 14,  3,  5,  2, 14,  5,  3,  3,  5,  5,  2,  3, 14, 14,
   15 |  15, 15,  6, 15,  2,  6, 15, 15,  6,  2,  3,  6,  3, 15,  2, 15,  3,
   16 |  16, 16,  2, 16,  2,  2,  2, 16,  4,  2,  2,  2,  2,  2,  2, 16,  2,
   17 |  17, 17, 13, 17, 11, 13,  7, 17, 13, 11,  5, 13,  3,  7, 11, 17,  2,

Prog

(PARI)
\\ Needs also code from A348041:
A348043sq(x, y) = A348041sq(x, x*y);
A348043list(up_to) = { my(v = vector(up_to), i=0); for(a=1, oo, for(col=1, a, i++; if(i > up_to, return(v)); v[i] = A348043sq(col, (a-(col-1))))); (v); };
v348043 = A348043list(up_to);
A348043(n) = v348043[n];

Crossrefs

Cf. A005940, A156552, A348041, A348042, A348044 (main diagonal).

Cf. A000027 (all columns k that are powers of two: k = 2^e, for e >= 0).

Sequence in context: A242359 A368485 A113126 * A138060 A023121 A136261

Adjacent sequences: A348040 A348041 A348042 * A348044 A348045 A348046

Keyword

nonn,tabl

Author

Antti Karttunen, Sep 27 2021

Status

approved