A081927 -id:A081927 - cp's OEIS frontend

A081926 Triangle read by rows in which n-th row gives n smallest numbers with digit sum n.

1, 2, 11, 3, 12, 21, 4, 13, 22, 31, 5, 14, 23, 32, 41, 6, 15, 24, 33, 42, 51, 7, 16, 25, 34, 43, 52, 61, 8, 17, 26, 35, 44, 53, 62, 71, 9, 18, 27, 36, 45, 54, 63, 72, 81, 19, 28, 37, 46, 55, 64, 73, 82, 91, 109, 29, 38, 47, 56, 65, 74, 83, 92, 119, 128, 137

Offset: 1

Amarnath Murthy, Apr 01 2003

			Triangle starts
1
2 11
3 12 21
4 13 22 31
5 14 23 32 41

Robert Israel, Table of n, a(n) for n = 1..10011 (first 141 rows, flattened; first 40 rows from T. D. Noe)

Cf. A081927, A081928.

f:= proc(n) local Res, d, v, count;
    Res:= NULL; count:= 0;
    for d from ceil(n/9) while count < n do
       v:= g(n,d,n-count,1);
       Res:= Res, op(v);
       count:= count + nops(v);
    od:
    Res
end proc:
g:= proc(n,d,remain) local rem, Res, j, j0, v;
      if remain = 0 then return [] else rem:= remain fi;
      if nargs = 4 then j0:= 1 else j0:= 0 fi;
      if d = 1 then if n >= j0 and n <= 9 then [n] else [] fi
      else
        Res:= NULL;
        for j from max(j0, ceil(n-9*(d-1))) to min(9,n) while rem > 0 do
          v:= map(t -> j*10^(d-1)+t, procname(n-j,d-1,rem));
          Res:= Res, op(v);
          rem:= rem - nops(v);
        od;
        [Res]
      fi
end proc:
for i from 1 to 25 do f(i) od; # Robert Israel, Feb 19 2018

Needs["Combinatorica`"]; Table[Take[Union[Flatten[Table[FromDigits /@ Permutations[PadRight[s, 6]], {s, Partitions[n, 9]}]]], n], {n, 40}] (* T. D. Noe, Mar 08 2013 *)

A181178 n-th zerofree positive number with digital sum n.

Original entry on oeis.org

1, 11, 21, 31, 41, 51, 61, 71, 81, 118, 137, 165, 193, 257, 294, 376, 467, 567, 676, 785, 894, 1399, 1778, 1986, 2887, 3869, 4869, 5878, 6887, 7896, 8959, 9968, 18798, 26998, 35999, 45999, 56899, 66989, 76998, 87799

Offset: 1

Jonathan Vos Post, Jan 25 2011

n-th value in n-th row of triangular array A069800 in which n-th row consists of numbers (excluding the digit 0) with digit sum n arranged in increasing numerical order.

For n > 376, a(n) has decimal representation xyy...y, where x = (n+1) mod 9 + 1, and among y's exactly two equal 8 and the rest equal 9. For example, a(377) = 1999999998999999999999999999999999989999999. - Max Alekseyev, Aug 20 2013

			a(1) = 1 because 1 is the 1st number with digital sum 1;
a(2) = 11 because 11 is the 2nd number with digital sum 2 {2,11};
a(3) = 21 because 21 is the 3rd (zerofree positive) number with digital sum 3 {3,12,21,111};
a(4) = 31 because 31 is the 4th (zerofree positive) number with digital sum 4 {4,13,22,31,112,121,211,1111}.

Zak Seidov, Table of n, a(n) for n = 1..70

Cf. A007953, A052382, A069800, A081927.

nn=50; c=Table[0,{nn}]; t=c; cnt=0; n=0; While[cnt

A081928 Sum of the n smallest numbers having the sum of their digits equal to n.

Original entry on oeis.org

1, 13, 36, 70, 115, 171, 238, 316, 405, 604, 868, 1197, 1591, 2158, 2844, 3829, 5140, 6939, 9415, 12100, 14994, 18493, 26062, 34650, 49414, 69535, 96534, 129412, 164299, 201195, 240154, 281122, 414036, 584635, 852634, 1212633, 1629532

Offset: 1

Amarnath Murthy, Apr 01 2003

Sum of n-th row of A081926.

			The two smallest numbers with digit sum 2 are 2 and 11, whose sum is 13.
For seven, 7+16+25+34+43+52+61=238.

Cf. A081926, A081927, A051865.

a[n_] := Module[{}, co = 0; in = 1; su = 0; While[co < n, If[Plus @@ IntegerDigits[in] == n, co++; su = su + in]; in++ ]; su]; Table[a[n], {n, 1, 30}] (Steinerberger)

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 19 2003

Edited by N. J. A. Sloane, Jul 02 2008 at the suggestion of R. J. Mathar

A263019 If n is the i-th positive integer with digital sum j, then a(n) is the j-th positive integer with digital sum i.

Original entry on oeis.org

1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 2, 11, 20, 101, 110, 200, 1001, 1010, 1100, 1000000000, 12, 21, 30, 102, 111, 120, 201, 210, 2000, 10000000000, 22, 31, 40, 103, 112, 121, 130, 300, 10001, 100000000000, 32, 41, 50, 104, 113, 122

Offset: 1

Paul Tek, Oct 07 2015

Digital sum is given by A007953.
This is a self-inverse permutation of the natural numbers, with fixed points A081927.
A007953(n) = A081927(a(n)) for any n>0.
A081927(n) = A007953(a(n)) for any n>0.
a(A051885(n)) = 10^(n-1) for any n>0.
a(10^(n-1)) = A051885(n) for any n>0.

Paul Tek, Table of n, a(n) for n = 1..10000
Paul Tek, PERL program for this sequence

Cf. A007953, A051885, A081927, A254524, A263018.

a(n) = {j = sumdigits(n); v = vector(n, k, sumdigits(k)); i = #select(x->x==j, v); nb = 0; k = 0; while(nb != j, k++; if (sumdigits(k) == i, nb++)); k;} \\ Michel Marcus, Oct 16 2015

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A081926 Triangle read by rows in which n-th row gives n smallest numbers with digit sum n.

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A181178 n-th zerofree positive number with digital sum n.

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A081928 Sum of the n smallest numbers having the sum of their digits equal to n.

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A263019 If n is the i-th positive integer with digital sum j, then a(n) is the j-th positive integer with digital sum i.

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