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A254055
Square array: A(row,col) = A003602(A254051(row,col)), read by antidiagonals A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), ...
6
1, 2, 1, 1, 1, 3, 2, 6, 12, 4, 4, 9, 1, 9, 21, 5, 3, 13, 48, 102, 31, 3, 7, 30, 75, 36, 10, 183, 2, 15, 39, 6, 112, 426, 912, 274, 7, 18, 22, 58, 264, 669, 160, 684, 1641, 8, 10, 7, 129, 345, 198, 1003, 3828, 8202, 2461, 1, 6, 57, 156, 193, 517, 2370, 6015, 2871, 3076, 14763, 5, 24, 66, 85, 117, 1155, 3099, 889, 9022, 34446, 73812, 22144
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 A135764(1,A(row+1,col)).
What the resulting odd number will be, is given by A254101(row+1,col).
EXAMPLE
The top left corner of the array:
1, 2, 1, 2, 4, 5, 3, 2, 7, 8, 1, ...
1, 1, 6, 9, 3, 7, 15, 18, 10, 6, 24, ...
3, 12, 1, 13, 30, 39, 22, 7, 57, 66, 18, ...
4, 9, 48, 75, 6, 58, 129, 156, 85, 25, 210, ...
21, 102, 36, 112, 264, 345, 193, 117, 507, 588, 79, ...
31, 10, 426, 669, 198, 517, 1155, 1398, 760, 441, 1884, ...
183, 912, 160, 1003, 2370, 3099, 1732, 66, 4557, 5286, 1413, ...
274, 684, 3828, 6015, 889, 4648, 10389, 12576, 6835, 496, 16950, ...
etc.
PROG
(Scheme, two versions)
(define (A254055 n) (A254055bi (A002260 n) (A004736 n)))
(define (A254055bi row col) (A003602 (A254051bi row col))) ;; A254051bi given in A254051.
(define (A254055v2 n) (A254055biv2 (A002260 n) (A004736 n)))
(define (A254055biv2 row col) (A003602 (A048673 (A135764bi row (A249745 col))))) ;; A135764bi given in A135764.
CROSSREFS
Related arrays: A135764, A135765, A254051, A254101, A254102.
Sequence in context: A302126 A136043 A336420 * A373367 A373362 A373145
KEYWORD
nonn,tabl
AUTHOR
Antti Karttunen, Jan 27 2015
STATUS
approved