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A348042
Square array A(n,k) = the nearest common ancestor of n, k and n*k in Doudna tree (A005940).
4
1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 2, 2, 1, 1, 2, 2, 2, 2, 1, 1, 2, 3, 4, 3, 2, 1, 1, 2, 2, 2, 2, 2, 2, 1, 1, 2, 3, 2, 2, 2, 3, 2, 1, 1, 2, 2, 2, 3, 3, 2, 2, 2, 1, 1, 2, 2, 4, 3, 2, 3, 4, 2, 2, 1, 1, 2, 3, 4, 2, 3, 3, 2, 4, 3, 2, 1, 1, 2, 3, 2, 2, 2, 2, 2, 2, 2, 3, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1
OFFSET
1,5
COMMENTS
Array is symmetric and is read by antidiagonals as A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), ...
FORMULA
A(n, k) = A(k, n).
A(n, k) = A348041(n*k, A348041(n, k)).
A(n, k) = A348041(n, A348043(k, n)) = A348041(k, A348043(n, k)).
For any two squares s=u^2 and t=v^2, A(s, t) is a square also.
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 | 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
3 | 1, 2, 2, 2, 3, 2, 3, 2, 2, 3, 3, 2, 3, 3, 3, 2, 3,
4 | 1, 2, 2, 4, 2, 2, 2, 4, 4, 2, 2, 2, 2, 2, 2, 4, 2,
5 | 1, 2, 3, 2, 2, 3, 3, 2, 2, 2, 5, 3, 5, 3, 2, 2, 5,
6 | 1, 2, 2, 2, 3, 2, 3, 2, 2, 3, 3, 2, 3, 3, 6, 2, 3,
7 | 1, 2, 3, 2, 3, 3, 2, 2, 2, 3, 3, 3, 5, 2, 3, 2, 7,
8 | 1, 2, 2, 4, 2, 2, 2, 8, 4, 2, 2, 2, 2, 2, 2, 8, 2,
9 | 1, 2, 2, 4, 2, 2, 2, 4, 4, 2, 2, 2, 2, 2, 2, 4, 2,
10 | 1, 2, 3, 2, 2, 3, 3, 2, 2, 2, 5, 3, 5, 3, 2, 2, 5,
11 | 1, 2, 3, 2, 5, 3, 3, 2, 2, 5, 2, 3, 3, 3, 3, 2, 5,
12 | 1, 2, 2, 2, 3, 2, 3, 2, 2, 3, 3, 2, 3, 3, 6, 2, 3,
13 | 1, 2, 3, 2, 5, 3, 5, 2, 2, 5, 3, 3, 2, 5, 3, 2, 3,
14 | 1, 2, 3, 2, 3, 3, 2, 2, 2, 3, 3, 3, 5, 2, 3, 2, 7,
15 | 1, 2, 3, 2, 2, 6, 3, 2, 2, 2, 3, 6, 3, 3, 2, 2, 3,
16 | 1, 2, 2, 4, 2, 2, 2, 8, 4, 2, 2, 2, 2, 2, 2, 16, 2,
17 | 1, 2, 3, 2, 5, 3, 7, 2, 2, 5, 5, 3, 3, 7, 3, 2, 2,
PROG
(PARI)
\\ Needs also code from A348041:
up_to = 105;
A348042sq(row, col) = A348041sq(row*col, A348041sq(row, col));
A348042list(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] = A348042sq(col, (a-(col-1))))); (v); };
v348042 = A348042list(up_to);
A348042(n) = v348042[n];
CROSSREFS
Cf. A005940, A156552, A348041, A348043, A348044 (main diagonal).
Sequence in context: A154325 A129765 A143187 * A143209 A163994 A355802
KEYWORD
nonn,tabl
AUTHOR
Antti Karttunen, Sep 27 2021
STATUS
approved