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

Author

Antti Karttunen, Jan 28 2015

Keywords

• nonn
• tabl

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).

Examples

			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.
		

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

Crossrefs

Cf. A000265, A126760, A253887, A254048.

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

Programs

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)))

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)).