A254101 Square array A(row,col) = A000265(A254051(row,col)).

1, 3, 1, 1, 1, 5, 3, 11, 23, 7, 7, 17, 1, 17, 41, 9, 5, 25, 95, 203, 61, 5, 13, 59, 149, 71, 19, 365, 3, 29, 77, 11, 223, 851, 1823, 547, 13, 35, 43, 115, 527, 1337, 319, 1367, 3281, 15, 19, 13, 257, 689, 395, 2005, 7655, 16403, 4921, 1, 11, 113, 311, 385, 1033, 4739, 12029, 5741, 6151, 29525

Offset

1,2

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 at the first row of array A135764 as x_new = A135764(1,A254055(row+1,col)) and it is given here as A(row+1,col) = A000265(A254051(row+1,col)).

That number's column index in array A135765 is then given by A254102(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) = A000265(A254051(row,col)).

A(row,col) = (2*A254055(row,col))-1.

A(row,col) = A003961(A254055(row, A249745(col))).

A(row+1,col) = A139391(A135765(row,col)).

As compositions of one-dimensional sequences:

a(n) = A000265(A254051(n)).

a(n) = (2*A254055(n))-1.

Example

The top left corner of the array:
    1,    3,    1,     3,    7,    9,     5,     3,    13,    15,     1, ...
    1,    1,   11,    17,    5,   13,    29,    35,    19,    11,    47, ...
    5,   23,    1,    25,   59,   77,    43,    13,   113,   131,    35, ...
    7,   17,   95,   149,   11,  115,   257,   311,   169,    49,   419, ...
   41,  203,   71,   223,  527,  689,   385,   233,  1013,  1175,   157, ...
   61,   19,  851,  1337,  395, 1033,  2309,  2795,  1519,   881,  3767, ...
  365, 1823,  319,  2005, 4739, 6197,  3463,   131,  9113, 10571,  2825, ...
  547, 1367, 7655, 12029, 1777, 9295, 20777, 25151, 13669,   991, 33899, ...
etc.

Prog

(Scheme)
(define (A254101 n) (A254101bi (A002260 n) (A004736 n)))
(define (A254101bi row col) (+ -1 (* 2 (A254055bi row col))))
;; Alternative definition:
(define (A254101v2 n) (A254101biv2 (A002260 n) (A004736 n)))
(define (A254101biv2 row col) (A003961 (A254055bi row (A249745 col))))

Crossrefs

Cf. A000265, A002260, A004736, A003961, A139391, A249745.

Related arrays: A135764, A135765, A254051, A254055, A254102.

Sequence in context: A046643 A369180 A351565 * A349025 A348963 A350470

Adjacent sequences: A254098 A254099 A254100 * A254102 A254103 A254104

Keyword

nonn,tabl

Author

Antti Karttunen, Jan 28 2015

Status

approved