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A254524 n is the a(n)-th positive integer having its digitsum. 18
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,10
COMMENTS
a(A051885(n)) = 1. - Reinhard Zumkeller, Oct 09 2015
Ordinal transform of A007953. - Antti Karttunen, May 20 2017
LINKS
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. A286478 (analogous sequence for factorial base).
Sequence in context: A259143 A035931 A330634 * A132211 A067441 A357299
KEYWORD
nonn,base,look,nice
AUTHOR
David A. Corneth, Jan 31 2015
STATUS
approved

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Last modified March 29 05:16 EDT 2024. Contains 371264 sequences. (Running on oeis4.)