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

1,1

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.

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

Example

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
...

Prog

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

Crossrefs

Row 1: A055938, Row 2: A257507.

Cf. A011371, A055938.

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

Sequence in context: A046527 A378764 A008343 * A093952 A308882 A079614

Adjacent sequences: A257261 A257262 A257263 * A257265 A257266 A257267

Keyword

nonn,tabl

Author

Antti Karttunen, May 03 2015

Status

approved