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

0,3

Comments

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

a(n) is a concatenation of positions on which 1s appear in the binary expansion of n, counting from the right. For example, the binary expansion of 1541 is 11000000101, with 1s appearing on the 1st, 3rd, 10th, and 11th positions. Hence, a(1541) = 131011. - Dmytro Inosov, Mar 21 2026

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

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)

Example

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

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 *)

Prog

(C) #include <stdio.h>
#include <stdlib.h>
#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

Crossrefs

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

Sequence in context: A072484 A337918 A113698 * A365703 A275841 A224841

Adjacent sequences: A048791 A048792 A048793 * A048795 A048796 A048797

Keyword

nonn,easy,nice,base

Author

N. J. A. Sloane

Extensions

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

Keyword base added by Reinhard Zumkeller, Nov 16 2013

Status

approved