A230093 Number of values of k such that k + (sum of digits of k) is n.

1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 2, 1

Offset

0,102

Comments

a(n) is the number of times n occurs in A062028.

For n>=1, a(10^n) = a(9*n-1). - Max Alekseyev, Feb 23 2021

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Index entries for Colombian or self numbers and related sequences

Maple

# Maple code for A062028, A230093, A003052, A225793, A230094.
with(LinearAlgebra):
read transforms; # to get digsum
M := 1000; A062028 := Array(0..M); A230093 := Array(0..M);
for n from 0 to M do
   m := n+digsum(n);
   A062028[n] := m;
   if m <= M then A230093[m] := A230093[m]+1; fi;
od:
t1:=[seq(A062028[i], i=0..M)]; # A062028 as list (but incorrect offset 1)
t2:=[seq(A230093[i], i=0..M)]; # A230093 as list, but then a(0) has index 1
# A003052 := COMPl(t1); # COMPl has issues, may be incorrect for M <> 1000
ctmax:=4;
for h from 0 to ctmax do ct[h] := []; od:
for i from 1 to M do
   h := lis2[i];
   if h <= ctmax then ct[h] := [op(ct[h]), i]; fi;
od:
A225793 := ct[1]; A230094 := ct[2]; # A003052 := ct[0]; # see there for better code

Mathematica

Module[{nn=110, a, b, c, d}, a=Tally[Table[x+Total[IntegerDigits[x]], {x, 0, nn}]]; b=a[[All, 1]]; c={#, 0}&/@Complement[Range[nn], b]; d=Sort[Join[a, c]]; d[[All, 2]]] (* Harvey P. Dale, Jun 12 2019 *)

Prog

(Haskell) a230093 n = length $ filter ((== n) . a062028) [n - 9 * a055642 n .. n]  -- Reinhard Zumkeller, Oct 11 2013
(PARI) apply( A230093(n)=sum(i=n>0, min(9*logint(n+!n, 10)+8, n\2), sumdigits(n-i)==i), [1..150]) \\ M. F. Hasler, Nov 08 2018

Crossrefs

Cf. A006064, A007953 (sum of digits), A062028 (n + sum of its digits), A004207, A228085, A003052, A176995, A225793, A230094, A055642.

Cf. A107740 (this applied to primes).

Sequence in context: A073520 A152137 A097470 * A033322 A329679 A130713

Adjacent sequences: A230090 A230091 A230092 * A230094 A230095 A230096

Keyword

nonn,base

Author

N. J. A. Sloane, Oct 10 2013

Extensions

Edited by M. F. Hasler, Nov 08 2018

Status

approved