cp's OEIS Frontend

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

%I A254102 #16 Feb 03 2015 16:10:45
%S A254102 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,
%T A254102 10,26,4,75,284,608,183,5,12,15,39,176,446,107,456,1094,2,7,5,86,230,
%U A254102 132,669,2552,5468,1641,1,4,38,104,129,345,1580,4010,1914,2051,9842
%N A254102 Square array A(row,col) = A253887(A254055(row,col)) = A126760(A254101(row,col)).
%C A254102 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)).
%C A254102 What the resulting odd number will be, is given by A254101(row+1,col) =  A000265(A254051(row+1,col)).
%C A254102 That number's column index in array A135765 is then given by A(row+1,col).
%H A254102 Antti Karttunen, <a href="/A254102/b254102.txt">Table of n, a(n) for n = 1..10440; the first 144 antidiagonals of array</a>
%H A254102 <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%F A254102 A(row,col) = A126760(A254051(row,col)) = A126760(A254101(row,col)).
%F A254102 A(row,col) = A253887(A254055(row,col)).
%F A254102 A(row+1,col) = A254048(A135765(row,col)).
%e A254102 The top left corner of the array:
%e A254102      1,    1,    1,    1,     3,     1,     2,    1,     5,     2,     1,
%e A254102      1,    1,    4,    6,     2,     5,    10,   12,     7,     4,    16,
%e A254102      2,    8,    1,    9,    20,    26,    15,    5,    38,    44,    12,
%e A254102      3,    6,   32,   50,     4,    39,    86,  104,    57,    17,   140,
%e A254102     14,   68,   24,   75,   176,   230,   129,   78,   338,   392,    53,
%e A254102     21,    7,  284,  446,   132,   345,   770,  932,   507,   294,  1256,
%e A254102    122,  608,  107,  669,  1580,  2066,  1155,   44,  3038,  3524,   942,
%e A254102    183,  456, 2552, 4010,   593,  3099,  6926, 8384,  4557,   331, 11300,
%e A254102   1094, 5468, 1914, 6015, 14216, 18590, 10389, 6288, 27338, 31712,   530,
%e A254102 etc.
%o A254102 (Scheme)
%o A254102 (define (A254102 n) (A254102bi (A002260 n) (A004736 n)))
%o A254102 ;; In turn using either one of these three bivariate functions:
%o A254102 (define (A254102 n) (A254102bi (A002260 n) (A004736 n)))
%o A254102 (define (A254102bi row col) (A126760 (A254051bi row col)))
%o A254102 (define (A254102bi row col) (A253887 (A254055bi row col)))
%o A254102 (define (A254102bi row col) (A126760 (A254101bi row col)))
%Y A254102 Cf. A000265, A126760, A253887, A254048.
%Y A254102 Related arrays: A135764, A135765, A254051, A254055, A254101.
%K A254102 nonn,tabl
%O A254102 1,6
%A A254102 _Antti Karttunen_, Jan 28 2015