A254524 n is the a(n)-th positive integer having its digitsum.

1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 3, 3, 3, 3, 3, 3, 3, 3, 2, 1, 4, 4, 4, 4, 4, 4, 4, 3, 2, 1, 5, 5, 5, 5, 5, 5, 4, 3, 2, 1, 6, 6, 6, 6, 6, 5, 4, 3, 2, 1, 7, 7, 7, 7, 6, 5, 4, 3, 2, 1, 8, 8, 8, 7, 6, 5, 4, 3, 2, 1, 9, 9, 8, 7, 6, 5, 4, 3, 2, 1, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 10, 5

Offset

1,10

Comments

a(A051885(n)) = 1. - Reinhard Zumkeller, Oct 09 2015

Ordinal transform of A007953. - Antti Karttunen, May 20 2017

Links

David A. Corneth, Table of n, a(n) for n = 1..10000

Example

35 is the 4th positive integer having digitsum 8 (the others before are 8, 17 and 26) so a(35) = 4.

Mathematica

c[n_, k_] := If[n >= k, Binomial[n, k], 0]; b[s_, q_, n_] := (s1 = q; If[s <= q*(n - 1), s1 = s + q; Sum[(-1)^i*c[q, i]*c[s1 - 1 - n*i, q - 1], {i, 0, q - 1}], 0]); a[n_] := (r = 1; v = IntegerDigits[n]; l = v[[-1]]; For[i = Length[v] - 1, i >= 1, i--, For[j = 1, j <= v[[i]], j++, r += b[l + j, Length[v] - i, 10]]; l += v[[i]]]; r); Table[a[n], {n, 1, 110}] (* Jean-François Alcover, Nov 14 2016, adapted from PARI *)
With[{nn=400}, #[[3]]&/@Sort[Flatten[Table[Flatten[#, 1]&/@MapIndexed[ List, Select[ Table[{n, Total[IntegerDigits[n]]}, {n, nn}], #[[2]]==k&]], {k, nn}], 1]]](* Harvey P. Dale, Mar 29 2020 *)

Prog

(PARI)
\\This algorithm needs a modified binomial.
C(n, k)=if(n>=k, binomial(n, k), 0)
\\ways to roll s-q with q dice having sides 0 through n - 1.
b(s, q, n)=if(s<=q*(n-1), s+=q; sum(i=0, q-1, (-1)^i*C(q, i)*C(s-1-n*i, q-1)), 0)
\\main algorithm
a(n)={r = 1; v=digits(n); l=v[#v]; forstep(i = #v-1, 1, -1, for(j=1, v[i], r+=b(l+j, #v-i, 10)); l+=v[i]); r}
(Haskell)
import Data.IntMap (empty, findWithDefault, insert)
a254524 n = a254524_list !! (n-1)
a254524_list = f 1 empty where
   f x m = y : f (x + 1) (insert q (y + 1) m) where
           y = findWithDefault 1 q m; q = a007953 x
-- Reinhard Zumkeller, Oct 09 2015

Crossrefs

Cf. A007953, A051885, A069877, A143164, A263017, A263109, A263110.

Cf. A286478 (analogous sequence for factorial base).

Sequence in context: A259143 A035931 A330634 * A374097 A132211 A067441

Adjacent sequences: A254521 A254522 A254523 * A254525 A254526 A254527

Keyword

nonn,base,look,nice

Author

David A. Corneth, Jan 31 2015

Status

approved