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%I #21 Feb 01 2015 09:59:51
%S 1,3,2,5,6,4,7,10,12,8,11,14,20,24,16,13,22,28,40,48,32,17,26,44,56,
%T 80,96,64,19,34,52,88,112,160,192,128,9,38,68,104,176,224,320,384,256,
%U 23,18,76,136,208,352,448,640,768,512,29,46,36,152,272,416,704,896,1280,1536,1024,15,58,92,72,304,544,832,1408,1792,2560,3072,2048,31,30
%N Square array: A(row,col) = 2^(row-1) * ((2*A249745(col))-1) = A064216(A254051(row,col)), read by antidiagonals A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), ...
%C Shares with A135764 and A253551 the property that A001511(n) = k for all terms n on row k and when going downward in each column, terms grow by doubling.
%H Antti Karttunen, <a href="/A254053/b254053.txt">Table of n, a(n) for n = 1..2080; the first 64 antidiagonals of the array</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A(row,col) = A135764(row, A249745(col)). [Is otherwise the same array as A135764, but the column positions have been permuted by A249745.]
%F A(row,col) = 2^(row-1) * ((2*A249745(col))-1) = 2^(row-1) * A254050(col). [The above expands to this.]
%F a(n) = A064989(A135765(n)).
%F As a composition of other permutations:
%F a(n) = A064216(A254051(n)). [As an array: A(row,col) = A064216(A254051(row,col)).]
%e The top left corner of the array:
%e 1, 3, 5, 7, 11, 13, 17, 19, 9, 23, 29, 15, 31, 37, 41, 43,
%e 2, 6, 10, 14, 22, 26, 34, 38, 18, 46, 58, 30, 62, 74, 82, 86,
%e 4, 12, 20, 28, 44, 52, 68, 76, 36, 92, 116, 60, 124, 148, 164, 172,
%e 8, 24, 40, 56, 88, 104, 136, 152, 72, 184, 232, 120, 248, 296, 328, 344,
%e 16, 48, 80, 112, 176, 208, 272, 304, 144, 368, 464, 240, 496, 592, 656, 688,
%e ...
%o (Scheme, several alternative versions)
%o (define (A254053 n) (A135764bi (A002260 n) (A249745 (A004736 n))))
%o (define (A254053 n) (* (A000079 (- (A002260 n) 1)) (+ -1 (* 2 (A249745 (A004736 n))))))
%o (define (A254053 n) (* (A000079 (- (A002260 n) 1)) (A254050 (A004736 n))))
%o (define (A254053bi row col) (A064216 (A254051bi row col)))
%o (define (A254053 n) (A254053bi (A002260 n) (A004736 n)))
%o (define (A254053 n) (A064216 (A254051 n)))
%Y Inverse: A254054.
%Y Similar or related permutations: A135764, A253551, A064216, A254051.
%Y Cf. A000079, A001511, A002260, A004736, A064989, A135765, A249745, A254049, A254050.
%K nonn,tabl
%O 1,2
%A _Antti Karttunen_, Jan 24 2015