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 A048793 List giving all subsets of natural numbers arranged in standard statistical (or Yates) order. 188
 0, 1, 2, 1, 2, 3, 1, 3, 2, 3, 1, 2, 3, 4, 1, 4, 2, 4, 1, 2, 4, 3, 4, 1, 3, 4, 2, 3, 4, 1, 2, 3, 4, 5, 1, 5, 2, 5, 1, 2, 5, 3, 5, 1, 3, 5, 2, 3, 5, 1, 2, 3, 5, 4, 5, 1, 4, 5, 2, 4, 5, 1, 2, 4, 5, 3, 4, 5, 1, 3, 4, 5, 2, 3, 4, 5, 1, 2, 3, 4, 5, 6, 1, 6, 2, 6, 1, 2, 6, 3, 6, 1, 3, 6, 2, 3, 6, 1, 2, 3, 6, 4, 6, 1, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS For n>0: first occurrence of n in row 2^(n-1), and when the table is seen as a flattened list at position n*2^(n-1)+1, cf. A005183. - Reinhard Zumkeller, Nov 16 2013 Row n lists the positions of 1's in the reversed binary expansion of n. Compare to triangles A112798 and A213925. - Gus Wiseman, Jul 22 2019 REFERENCES S. Hedayat, N. J. A. Sloane and J. Stufken, Orthogonal Arrays, Springer-Verlag, NY, 1999, p. 249. LINKS Reinhard Zumkeller, Rows n = 0..1000 of triangle, flattened FORMULA Constructed recursively: subsets that include n are obtained by appending n to all earlier subsets. EXAMPLE From Gus Wiseman, Jul 22 2019: (Start) Triangle begins:   {}   1   2   1  2   3   1  3   2  3   1  2  3   4   1  4   2  4   1  2  4   3  4   1  3  4   2  3  4   1  2  3  4   5   1  5   2  5   1  2  5   3  5 (End) MAPLE T:= proc(n) local i, l, m; l:= NULL; m:= n;       if n=0 then return 0 fi; for i while m>0 do       if irem(m, 2, 'm')=1 then l:=l, i fi od; l     end: seq(T(n), n=1..50);  # Alois P. Heinz, Sep 06 2014 MATHEMATICA s = {{}}; s[n_] := s[n] = Join[s[n - 1], Append[#, n]& /@ s[n - 1]]; Join[{0}, Flatten[s]] (* Jean-François Alcover, May 24 2012 *) Table[Join@@Position[Reverse[IntegerDigits[n, 2]], 1], {n, 30}] (* Gus Wiseman, Jul 22 2019 *) PROG (C) #include #include #define USAGE "Usage: 'A048793 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 short 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); 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; new_row = 2;   for (i = 2; i <= end; i++) {     a[new_row++ ] = i;     for (old_row = 1; a[old_row] != i; old_row++) {       for (j = 0; a[old_row][j] != 0; j++) { a[new_row][j] = a[old_row][j]; }       a[new_row++ ][j] = i;     }   }   fprintf(stdout, "Values: 0");   for (i = 1; a[i] != 0; i++) for (j = 0; a[i][j] != 0; j++) fprintf(stdout, ", %d", a[i][j]);   fprintf(stdout, "\n"); return EXIT_SUCCESS } (Haskell) a048793 n k = a048793_tabf !! n !! k a048793_row n = a048793_tabf !! n a048793_tabf =  :  : f [] where    f xss = yss ++ f (xss ++ yss) where      yss = [y] : map (++ [y]) xss      y = last (last xss) + 1 -- Reinhard Zumkeller, Nov 16 2013 CROSSREFS Cf. A048794. Row lengths are A000120. First column is A001511. Row sums are A029931. Reversing rows gives A272020. Subtracting 1 from each term gives A133457; subtracting 1 and reversing rows gives A272011. Indices of relatively prime rows are A291166 (see also A326674); arithmetic progressions are A295235; rows with integer average are A326669 (see also A326699/A326700); pairwise coprime rows are A326675. Cf. A035327, A070939. Sequence in context: A002343 A082076 A231516 * A344084 A249783 A209278 Adjacent sequences:  A048790 A048791 A048792 * A048794 A048795 A048796 KEYWORD nonn,tabf,easy,nice AUTHOR EXTENSIONS More terms from Larry Reeves (larryr(AT)acm.org), Apr 11 2000 STATUS approved

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Last modified June 15 04:47 EDT 2021. Contains 345043 sequences. (Running on oeis4.)