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%I #16 Feb 03 2015 16:10:45
%S 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 10,26,4,75,284,608,183,5,12,15,39,176,446,107,456,1094,2,7,5,86,230,
%U 132,669,2552,5468,1641,1,4,38,104,129,345,1580,4010,1914,2051,9842
%N Square array A(row,col) = A253887(A254055(row,col)) = A126760(A254101(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 A135764(1,A254055(row+1,col)).
%C What the resulting odd number will be, is given by A254101(row+1,col) = A000265(A254051(row+1,col)).
%C That number's column index in array A135765 is then given by A(row+1,col).
%H Antti Karttunen, <a href="/A254102/b254102.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) = A126760(A254051(row,col)) = A126760(A254101(row,col)).
%F A(row,col) = A253887(A254055(row,col)).
%F A(row+1,col) = A254048(A135765(row,col)).
%e The top left corner of the array:
%e 1, 1, 1, 1, 3, 1, 2, 1, 5, 2, 1,
%e 1, 1, 4, 6, 2, 5, 10, 12, 7, 4, 16,
%e 2, 8, 1, 9, 20, 26, 15, 5, 38, 44, 12,
%e 3, 6, 32, 50, 4, 39, 86, 104, 57, 17, 140,
%e 14, 68, 24, 75, 176, 230, 129, 78, 338, 392, 53,
%e 21, 7, 284, 446, 132, 345, 770, 932, 507, 294, 1256,
%e 122, 608, 107, 669, 1580, 2066, 1155, 44, 3038, 3524, 942,
%e 183, 456, 2552, 4010, 593, 3099, 6926, 8384, 4557, 331, 11300,
%e 1094, 5468, 1914, 6015, 14216, 18590, 10389, 6288, 27338, 31712, 530,
%e etc.
%o (Scheme)
%o (define (A254102 n) (A254102bi (A002260 n) (A004736 n)))
%o ;; In turn using either one of these three bivariate functions:
%o (define (A254102 n) (A254102bi (A002260 n) (A004736 n)))
%o (define (A254102bi row col) (A126760 (A254051bi row col)))
%o (define (A254102bi row col) (A253887 (A254055bi row col)))
%o (define (A254102bi row col) (A126760 (A254101bi row col)))
%Y Cf. A000265, A126760, A253887, A254048.
%Y Related arrays: A135764, A135765, A254051, A254055, A254101.
%K nonn,tabl
%O 1,6
%A _Antti Karttunen_, Jan 28 2015
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