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A081927 n-th positive integer whose digits sum up to n. 5
1, 11, 21, 31, 41, 51, 61, 71, 81, 109, 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, 97889, 178899, 199798, 298988, 398988 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Robert Israel, Table of n, a(n) for n = 1..8989

FORMULA

From Robert Israel, Feb 20 2018: (Start)

a(9*k-j) = (12-j)*10^(k-1) - 10^(k-10) - 10^(j+k-45) - 1 for j=2..9, k >= 45-j.

a(9*k-1) = 2*10^k - 10^(k-9) - 10^(k-35) - 1, k >= 35. (End)

EXAMPLE

31 is the 4th integer of the sequence and the 4th number whose digits sum up to 4 : 4, 13, 22, [31], 103, 112, 121, 130, ...

109 is the 10th integer of the sequence and the 10th number whose digits sum up to 10 : 19, 28, 37, 46, 55, 64, 73, 82, 91, [109], 118, 127, 136, ...

MAPLE

f:= proc(n) local Res, d, v, count;

    count:= 0;

    for d from ceil(n/9) while count < n do

       v:= g(n, d, n-count, 1);

       Res:= v[-1];

       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:

map(f, [$1..200]); # Robert Israel, Feb 19 2018

CROSSREFS

Leading diagonal of A081926.

Cf. A081928, A181178

Sequence in context: A017281 A061589 A110402 * A181178 A178205 A239464

Adjacent sequences:  A081924 A081925 A081926 * A081928 A081929 A081930

KEYWORD

base,nonn

AUTHOR

Amarnath Murthy, Apr 01 2003

EXTENSIONS

Corrected and extended by Ray Chandler, Oct 29 2003

STATUS

approved

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Last modified July 21 00:49 EDT 2019. Contains 325189 sequences. (Running on oeis4.)