OFFSET
1,1
COMMENTS
Like Keith numbers but starting from 9*n digits to reach n.
Consider the digits of 9*n. Take their sum and repeat the process deleting the first addend and adding the previous sum. The sequence lists the numbers that after some iterations reach a sum equal to themselves.
EXAMPLE
9*17 = 153:
1 + 5 + 3 = 9;
5 + 3 + 9 = 17.
MAPLE
with(numtheory): P:=proc(q, h, w) local a, b, k, n, t, v; v:=array(1..h);
for n from 1 to q do a:=w*n; b:=ilog10(a)+1; if b>1 then
for k from 1 to b do v[b-k+1]:=(a mod 10); a:=trunc(a/10); od; t:=b+1; v[t]:=add(v[k], k=1..b); while v[t]<n do t:=t+1; v[t]:=add(v[k], k=t-b..t-1); od;
if v[t]=n then print(n); fi; fi; od; end: P(10^6, 1000, 9);
MATHEMATICA
Select[Range[10^6], Function[n, Module[{d = IntegerDigits[9 n], s, k = 0}, s = Total@ d; While[s < n, AppendTo[d, s]; k++; s = 2 s - d[[k]]]; s == n]]] (* Michael De Vlieger, Feb 22 2017, after T. D. Noe at A007629 *)
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Paolo P. Lava, Feb 22 2017
STATUS
approved