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

Author

Antti Karttunen, Sep 27 2021

Keywords

• nonn
• tabl

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), ...

Examples

			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,
		

Links

• Index entries for sequences computed from indices in prime factorization

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).

Programs

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];

Formula

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