A254102 Square array A(row,col) = A253887(A254055(row,col)) = A126760(A254101(row,col)).

1, 1, 1, 1, 1, 2, 1, 4, 8, 3, 3, 6, 1, 6, 14, 1, 2, 9, 32, 68, 21, 2, 5, 20, 50, 24, 7, 122, 1, 10, 26, 4, 75, 284, 608, 183, 5, 12, 15, 39, 176, 446, 107, 456, 1094, 2, 7, 5, 86, 230, 132, 669, 2552, 5468, 1641, 1, 4, 38, 104, 129, 345, 1580, 4010, 1914, 2051, 9842

Offset

1,6

Comments

Starting with an odd number x = A135765(row,col), the result after one combined Collatz step (3x+1)/2 is found in A254051(row+1,col), and after iterated [i.e., we divide all powers of 2 out] Collatz step: x_new <- A139391(x) = A000265(3x+1) the resulting odd number x_new is located A135764(1,A254055(row+1,col)).

What the resulting odd number will be, is given by A254101(row+1,col) = A000265(A254051(row+1,col)).

That number's column index in array A135765 is then given by A(row+1,col).

Links

Antti Karttunen, Table of n, a(n) for n = 1..10440; the first 144 antidiagonals of array

Index entries for sequences related to 3x+1 (or Collatz) problem

Formula

A(row,col) = A126760(A254051(row,col)) = A126760(A254101(row,col)).

A(row,col) = A253887(A254055(row,col)).

A(row+1,col) = A254048(A135765(row,col)).

Example

The top left corner of the array:
     1,    1,    1,    1,     3,     1,     2,    1,     5,     2,     1,
     1,    1,    4,    6,     2,     5,    10,   12,     7,     4,    16,
     2,    8,    1,    9,    20,    26,    15,    5,    38,    44,    12,
     3,    6,   32,   50,     4,    39,    86,  104,    57,    17,   140,
    14,   68,   24,   75,   176,   230,   129,   78,   338,   392,    53,
    21,    7,  284,  446,   132,   345,   770,  932,   507,   294,  1256,
   122,  608,  107,  669,  1580,  2066,  1155,   44,  3038,  3524,   942,
   183,  456, 2552, 4010,   593,  3099,  6926, 8384,  4557,   331, 11300,
  1094, 5468, 1914, 6015, 14216, 18590, 10389, 6288, 27338, 31712,   530,
etc.

Prog

(Scheme)
(define (A254102 n) (A254102bi (A002260 n) (A004736 n)))
;; In turn using either one of these three bivariate functions:
(define (A254102 n) (A254102bi (A002260 n) (A004736 n)))
(define (A254102bi row col) (A126760 (A254051bi row col)))
(define (A254102bi row col) (A253887 (A254055bi row col)))
(define (A254102bi row col) (A126760 (A254101bi row col)))

Crossrefs

Cf. A000265, A126760, A253887, A254048.

Related arrays: A135764, A135765, A254051, A254055, A254101.

Sequence in context: A128411 A216046 A164614 * A094511 A209060 A193730

Adjacent sequences: A254099 A254100 A254101 * A254103 A254104 A254105

Keyword

nonn,tabl

Author

Antti Karttunen, Jan 28 2015

Status

approved