login
Transpose of square array A265345.
3

%I #11 Sep 20 2016 13:27:56

%S 1,2,3,4,6,7,8,12,10,5,16,24,20,22,9,64,48,40,28,18,21,32,192,80,56,

%T 36,30,13,184,96,160,112,72,60,26,19,352,552,640,224,144,120,52,14,25,

%U 704,1056,320,448,576,240,208,76,46,11,1408,2112,1600,1720,288,480,104,136,68,58,15

%N Transpose of square array A265345.

%C Square array A(row,col) is read by downwards antidiagonals as: A(0,0), A(0,1), A(1,0), A(0,2), A(1,1), A(2,0), A(0,3), A(1,2), A(2,1), A(3,0), ...

%C All the terms in the same row are either all divisible by 3, or none of them are.

%C Sequence A265345 is the main entry for this idea, please see further comment there.

%H Antti Karttunen, <a href="/A265347/b265347.txt">Table of n, a(n) for n = 1..2145; the antidiagonals 0 .. 64 of the array</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%e The top left corner of the array:

%e 1, 2, 4, 8, 16, 64, 32, 184, 352, 704, 1408, ...

%e 3, 6, 12, 24, 48, 192, 96, 552, 1056, 2112, 4224, ...

%e 7, 10, 20, 40, 80, 160, 640, 320, 1600, 3520, 6080, ...

%e 5, 22, 28, 56, 112, 224, 448, 1720, 824, 4936, 9856, ...

%e 9, 18, 36, 72, 144, 576, 288, 1656, 3168, 6336, 12672, ...

%e 21, 30, 60, 120, 240, 480, 1920, 960, 4800, 10560, 18240, ...

%e 13, 26, 52, 208, 104, 520, 1144, 2072, 3712, 16120, 6968, ...

%e 19, 14, 76, 136, 200, 256, 512, 1024, 6040, 3992, 15424, ...

%e 25, 46, 68, 88, 496, 344, 1984, 1376, 5344, 7768, 15224, ...

%e 11, 58, 44, 232, 424, 608, 736, 4384, 2936, 17536, 11744, ...

%e ...

%o (Scheme)

%o (define (A265347 n) (A265345bi (A025581 (+ -1 n)) (A002262 (+ -1 n)))) ;; o=1. Transpose of A265345.

%Y Inverse permutation: A265348.

%Y Transpose: A265345.

%K nonn,tabl,base

%O 1,2

%A _Antti Karttunen_, Dec 18 2015