A048794 Subsets of natural numbers arranged in standard statistical (or Yates) order.

0, 1, 2, 12, 3, 13, 23, 123, 4, 14, 24, 124, 34, 134, 234, 1234, 5, 15, 25, 125, 35, 135, 235, 1235, 45, 145, 245, 1245, 345, 1345, 2345, 12345, 6, 16, 26, 126, 36, 136, 236, 1236, 46, 146, 246, 1246, 346, 1346, 2346, 12346, 56, 156, 256, 1256, 356, 1356

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• nice
• base

Comments

a(2^n) = n+1. - Reinhard Zumkeller, Nov 16 2013

Examples

			empty; 1; 2; 1 2; 3; 1 3; 2 3; 1 2 3;...
		

References

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

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Crossrefs

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

Programs

C

#include 
#include 
#define USAGE "Usage: 'A048794 num' where num is the largest number to use creating sets.\n"
#define MAX_NUM 10
#define MAX_ROW 1024
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; }

Haskell

a048794 n = a048794_list !! n
a048794_list = map (read . concatMap show) a048793_tabf :: [Integer]
-- Reinhard Zumkeller, Nov 16 2013

Maple

a:= n-> (l-> parse(cat(0, seq(`if`(l[i]=1, i, [][])
             , i=1..nops(l)))))(Bits[Split](n)):
seq(a(n), n=0..53);  # Alois P. Heinz, Feb 01 2023

Mathematica

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 *)

Formula

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

From Alois P. Heinz, Feb 02 2023: (Start)

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

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

Extensions

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

Keyword base added by Reinhard Zumkeller, Nov 16 2013