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

Author

N. J. A. Sloane, Oct 10 2013

Keywords

• nonn
• base

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

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).

Programs

Haskell

a230093 n = length $ filter ((== n) . a062028) [n - 9 * a055642 n .. n]  -- Reinhard Zumkeller, Oct 11 2013

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 *)

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

Extensions

Edited by M. F. Hasler, Nov 08 2018