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A254053 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), ...

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