A257264 Square array A(row,col) read by antidiagonals: A(1,col) = A055938(col), and for row > 1, A(row,col) = A011371(A(row-1,col)).

2, 5, 1, 6, 3, 0, 9, 4, 1, 0, 12, 7, 3, 0, 0, 13, 10, 4, 1, 0, 0, 14, 10, 8, 3, 0, 0, 0, 17, 11, 8, 7, 1, 0, 0, 0, 20, 15, 8, 7, 4, 0, 0, 0, 0, 21, 18, 11, 7, 4, 3, 0, 0, 0, 0, 24, 18, 16, 8, 4, 3, 1, 0, 0, 0, 0, 27, 22, 16, 15, 7, 3, 1, 0, 0, 0, 0, 0, 28, 23, 19, 15, 11, 4, 1, 0, 0, 0, 0, 0, 0, 29, 25, 19, 16, 11, 8, 3, 0, 0, 0, 0, 0, 0, 0

Offset: 1

Author

Antti Karttunen, May 03 2015

Keywords

• nonn
• tabl

Comments

The array is read by 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 A011371, when starting from A055938(n), thus stepping through successive parent-nodes when starting from the n-th leaf of binary beanstalk, until finally reaching the fixed point 0, which is the root of the whole binary tree.

The hanging tails of columns (upward from the first encountered zero) converge towards A179016.

Examples

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

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10440; the first 144 antidiagonals of the array
• Paul Tek, Illustration of how natural numbers in range 0 .. 133 are organized as a binary tree in the binary beanstalk

Crossrefs

Row 1: A055938, Row 2: A257507.

Cf. A011371, A055938.

Cf. also A071542, A179016, A218254, A256993, A256997, A257265.

Programs

Scheme

(define (A257264 n) (A257264bi (A002260 n) (A004736 n)))
(define (A257264bi row col) (if (= 1 row) (A055938 col) (A011371 (A257264bi (- row 1) col))))