A262898 Square array A(row,col) read by antidiagonals: A(1,col) = A045765(col); for row > 1, if A(row-1,col) = 0 then A(row,col) = 0, otherwise A(row,col) = A049820(A(row-1,col)).

7, 8, 5, 13, 4, 3, 19, 11, 1, 1, 20, 17, 9, 0, 0, 24, 14, 15, 6, 0, 0, 25, 16, 10, 11, 2, 0, 0, 28, 22, 11, 6, 9, 0, 0, 0, 33, 22, 18, 9, 2, 6, 0, 0, 0, 36, 29, 18, 12, 6, 0, 2, 0, 0, 0, 37, 27, 27, 12, 6, 2, 0, 0, 0, 0, 0, 40, 35, 23, 23, 6, 2, 0, 0, 0, 0, 0, 0, 43, 32, 31, 21, 21, 2, 0, 0, 0, 0, 0, 0, 0, 49, 41, 26, 29, 17, 17, 0, 0, 0, 0, 0, 0, 0, 0, 50, 46, 39, 22, 27, 15, 15, 0, 0, 0, 0, 0, 0, 0, 0

Offset

1,1

Comments

The array is read by downwards antidiagonals: A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), etc.

Column n gives the trajectory of iterates of A049820, when starting from A045765(n), thus stepping through successive parent-nodes when starting from the n-th leaf in the tree generated by edge-relation A049820(child) = parent, until finally reaching the fixed point 0, which is the root of the whole tree.

A portion of the hanging tail of each column (upward from the first encountered zero) converges towards A259934, although not in monotone fashion.

Links

Antti Karttunen, Table of n, a(n) for n = 1..5050; the first 100 antidiagonals of the array

Formula

A(1,col) = A045765(col), and for row > 1, if A(row-1,col) = 0 then A(row,col) = 0, otherwise A(row,col) = A049820(A(row-1,col)).

Example

The top left corner of the array:
7, 8, 13, 19, 20, 24, 25, 28, 33, 36, 37, 40, 43, 49, 50, 52, 55, 56
5, 4, 11, 17, 14, 16, 22, 22, 29, 27, 35, 32, 41, 46, 44, 46, 51, 48
3, 1,  9, 15, 10, 11, 18, 18, 27, 23, 31, 26, 39, 42, 38, 42, 47, 38
1, 0,  6, 11,  6,  9, 12, 12, 23, 21, 29, 22, 35, 34, 34, 34, 45, 34
0, 0,  2,  9,  2,  6,  6,  6, 21, 17, 27, 18, 31, 30, 30, 30, 39, 30
0, 0,  0,  6,  0,  2,  2,  2, 17, 15, 23, 12, 29, 22, 22, 22, 35, 22
0, 0,  0,  2,  0,  0,  0,  0, 15, 11, 21,  6, 27, 18, 18, 18, 31, 18
0, 0,  0,  0,  0,  0,  0,  0, 11,  9, 17,  2, 23, 12, 12, 12, 29, 12
0, 0,  0,  0,  0,  0,  0,  0,  9,  6, 15,  0, 21,  6,  6,  6, 27,  6
0, 0,  0,  0,  0,  0,  0,  0,  6,  2, 11,  0, 17,  2,  2,  2, 23,  2
0, 0,  0,  0,  0,  0,  0,  0,  2,  0,  9,  0, 15,  0,  0,  0, 21,  0
0, 0,  0,  0,  0,  0,  0,  0,  0,  0,  6,  0, 11,  0,  0,  0, 17,  0
0, 0,  0,  0,  0,  0,  0,  0,  0,  0,  2,  0,  9,  0,  0,  0, 15,  0
0, 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  6,  0,  0,  0, 11,  0
0, 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  2,  0,  0,  0,  9,  0
0, 0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  6,  0
...

Prog

(Scheme)
(define (A262898 n) (A262898bi (A002260 n) (A004736 n)))
(define (A262898bi row col) (if (= 1 row) (A045765 col) (if (zero? (A262898bi (- row 1) col)) 0 (A049820 (A262898bi (- row 1) col)))))

Crossrefs

Transpose: A262899.

Cf. A045765 (row 1), A262902 (row 2).

Cf. A049820, A259934.

Cf. also A257264.

Sequence in context: A021060 A117239 A198365 * A004496 A197762 A181624

Adjacent sequences: A262895 A262896 A262897 * A262899 A262900 A262901

Keyword

nonn,tabl

Author

Antti Karttunen, Oct 06 2015

Status

approved