A048794 - OEIS

%I #28 Nov 29 2023 11:02:36

%S 0,1,2,12,3,13,23,123,4,14,24,124,34,134,234,1234,5,15,25,125,35,135,

%T 235,1235,45,145,245,1245,345,1345,2345,12345,6,16,26,126,36,136,236,

%U 1236,46,146,246,1246,346,1346,2346,12346,56,156,256,1256,356,1356

%N Subsets of natural numbers arranged in standard statistical (or Yates) order.

%C a(2^n) = n+1. - _Reinhard Zumkeller_, Nov 16 2013

%D S. Hedayat, N. J. A. Sloane and J. Stufken, Orthogonal Arrays, Springer-Verlag, NY, 1999, p. 249.

%H Reinhard Zumkeller, <a href="/A048794/b048794.txt">Table of n, a(n) for n = 0..10000</a>

%F Constructed recursively: subsets that include n are obtained by appending n to all earlier subsets.

%F From _Alois P. Heinz_, Feb 02 2023: (Start)

%F a(floor(2^(n-1))) = a(A131577(n)) = n.

%F a(2^n-1) = a(A000225(n)) = A007908(n) for n>=1. (End)

%e empty; 1; 2; 1 2; 3; 1 3; 2 3; 1 2 3;...

%p a:= n-> (l-> parse(cat(0, seq(`if`(l[i]=1, i, [][])

%p              , i=1..nops(l)))))(Bits[Split](n)):

%p seq(a(n), n=0..53);  # _Alois P. Heinz_, Feb 01 2023

%t nmax = 6; s[0] = {{}}; s[n_] := s[n] = Join[s[n-1], Append[#, n]& /@ s[n-1]]; FromDigits /@ s[nmax] (* _Jean-François Alcover_, Nov 15 2011 *)

%o (C) #include <stdio.h>

%o #include <stdlib.h>

%o #define USAGE "Usage: 'A048794 num' where num is the largest number to use creating sets.\n"

%o #define MAX_NUM 10

%o #define MAX_ROW 1024

%o int main(int argc, char *argv[]) { unsigned char a[MAX_ROW][MAX_NUM]; signed short old_row, new_row, i, j, end; if (argc < 2) { fprintf(stderr, USAGE); return EXIT_FAILURE; } end = atoi(argv[1]); end = (end > MAX_NUM) ? MAX_NUM: end; for (i = 0; i < MAX_ROW; i++) for ( j = 0; j < MAX_NUM; j++) a[i][j] = 0; a[1][0] = '1'; new_row = 2; for (i = 2; i <= end; i++) { sprintf(&a[new_row++ ][0], "%d", i); for (old_row = 1; a[old_row][0] != (i+48); old_row++) { sprintf(&a[new_row++ ][0], "%s%d", &a[old_row][0], i); } } fprintf(stdout, "Values: 0"); for (i = 1; a[i][0] != 0; i++) fprintf(stdout, ",%s", &a[i][0]); fprintf(stdout, "\n"); return EXIT_SUCCESS; }

%o (Haskell)

%o a048794 n = a048794_list !! n

%o a048794_list = map (read . concatMap show) a048793_tabf :: [Integer]

%o -- _Reinhard Zumkeller_, Nov 16 2013

%Y Cf. A000027, A000225, A007908, A048793, A131577.

%K nonn,easy,nice,base

%O 0,3

%A _N. J. A. Sloane_

%E More terms from Larry Reeves (larryr(AT)acm.org), Apr 11 2000

%E Keyword base added by _Reinhard Zumkeller_, Nov 16 2013