|
%I #14 Oct 01 2023 10:28:02
%S 1,2,3,4,6,5,8,9,10,7,16,12,15,14,11,32,18,20,21,22,13,64,24,30,28,33,
%T 26,17,128,27,25,42,44,39,34,19,256,48,40,35,66,52,51,38,23,512,36,45,
%U 56,55,78,68,57,46,29,1024,96,50,63,88,65,102,76,69,58,31,2048,54,80,70
%N Self-similar table, read by antidiagonals, where the k-th row is the product of the k-th prime with the antidiagonals of the first k rows of the table.
%C A permutation of the natural numbers.
%e 1st row lists the powers of 2 in ascending order starting with 1;
%e 2nd row = [3, 6, 9, 12, 18, 24, 27, 48, 36, 96, 54, 192, 72, 384, 81, ...] = 3*[1, 2, 3, 4, 6, 8, 9, 16, 12, 32, 18, 64, 24, 128, 27, ...];
%e 3rd row = [5, 10, 15, 20, 30, 25, 40, 45, 50, 80, 60, 75, 160, 90, 100, ...] = 5*[1, 2, 3, 4, 6, 5, 8, 9, 10, 16, 12, 15, 32, 18, 20, ...];
%e 4th row = [7, 14, 21, 28, 42, 35, 56, 63, 70, 49, 112, 84, 105, 98, ...] = 7*[1, 2, 3, 4, 6, 5, 8, 9, 10, 7, 16, 12, 15, 14, 32, 18, 20, 21, ...];
%e etc.
%e Table begins:
%e 1,2,4,8,16,32,64,128,256,512,1024,2048,...
%e 3,6,9,12,18,24,27,48,36,96,54,192,72,384,81,...
%e 5,10,15,20,30,25,40,45,50,80,60,75,160,90,...
%e 7,14,21,28,42,35,56,63,70,49,112,84,105,98,...
%e 11,22,33,44,66,55,88,99,110,77,176,132,...
%e 13,26,39,52,78,65,104,117,130,91,208,156,...
%e 17,34,51,68,102,85,136,153,170,119,272,204,...
%e ...
%Y Cf. A084288 (antidiagonal sums).
%K tabl,nonn
%O 1,2
%A _Paul D. Hanna_, May 25 2003
|
