A254101 - OEIS

%I #17 Feb 03 2015 16:10:23

%S 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,

%T 19,365,3,29,77,11,223,851,1823,547,13,35,43,115,527,1337,319,1367,

%U 3281,15,19,13,257,689,395,2005,7655,16403,4921,1,11,113,311,385,1033,4739,12029,5741,6151,29525

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

%C 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)).

%C That number's column index in array A135765 is then given by A254102(row+1,col).

%H Antti Karttunen, <a href="/A254101/b254101.txt">Table of n, a(n) for n = 1..10440; the first 144 antidiagonals of array</a>

%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>

%F A(row,col) = A000265(A254051(row,col)).

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

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

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

%F As compositions of one-dimensional sequences:

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

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

%e The top left corner of the array:

%e     1,    3,    1,     3,    7,    9,     5,     3,    13,    15,     1, ...

%e     1,    1,   11,    17,    5,   13,    29,    35,    19,    11,    47, ...

%e     5,   23,    1,    25,   59,   77,    43,    13,   113,   131,    35, ...

%e     7,   17,   95,   149,   11,  115,   257,   311,   169,    49,   419, ...

%e    41,  203,   71,   223,  527,  689,   385,   233,  1013,  1175,   157, ...

%e    61,   19,  851,  1337,  395, 1033,  2309,  2795,  1519,   881,  3767, ...

%e   365, 1823,  319,  2005, 4739, 6197,  3463,   131,  9113, 10571,  2825, ...

%e   547, 1367, 7655, 12029, 1777, 9295, 20777, 25151, 13669,   991, 33899, ...

%e etc.

%o (Scheme)

%o (define (A254101 n) (A254101bi (A002260 n) (A004736 n)))

%o (define (A254101bi row col) (+ -1 (* 2 (A254055bi row col))))

%o ;; Alternative definition:

%o (define (A254101v2 n) (A254101biv2 (A002260 n) (A004736 n)))

%o (define (A254101biv2 row col) (A003961 (A254055bi row (A249745 col))))

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

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

%K nonn,tabl

%O 1,2

%A _Antti Karttunen_, Jan 28 2015