A194854 Starting from a(1)=1, describe previous terms and then add all the digits.

1, 2, 5, 11, 13, 18, 28, 30, 32, 34, 40, 42, 44, 46, 54, 56, 58, 60, 62, 64, 66, 68, 70, 79, 90, 92, 94, 96, 98, 100, 103, 106, 100, 94, 87, 89, 91, 84, 86, 88, 81, 83, 85, 87, 89, 82, 84, 86, 88, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 104, 107, 110, 113

Offset: 1

Author

Paolo P. Lava, Sep 07 2011

Keywords

• nonn
• base

Examples

			Start with 1. There is one 1: 11 and 1+1=2. The sequence is now 1,2. Therefore one 1 and one 2: 1112 and 1+1+1+2=5. The sequence is now 1,2,5. Again: 111215 and 1+1+1+2+1+5=11. And so on.
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..10000
• Paolo P. Lava, Plot of the first 10000 terms of the sequence

Crossrefs

Cf. A045918, A063850, A138484-A138493

Programs

Maple

sd:=proc(j)
local c,d,h,k;
h:=j; c:=0;
if h>0 then
   d:=floor(evalf(log10(h))+1);
   for k from 1 to d do c:=c+h-10*trunc(h/10); h:=trunc(h/10); od;
fi;
c;
end:
P:=proc(i)
local a,b,f,n,p,s,v;
v:=array[10]; v[1]:=1; v[10]:=0; print(v[1]);
for n from 2 to 9 do v[n]:=0; od;
for n from 1 by 1 to i do
   a:=0;
   for p from 1 to 10 do
     if sd(v[p])=0 then a:=a+sd(v[p]);
     else a:=a+(p mod 10)+sd(v[p]);
     fi;
   od;
   print(a); s:=floor(evalf(log10(a))+1);
   for p from 1 to s do
     f:=a-10*trunc(a/10); a:=trunc(a/10);
     if f=0 then v[10]:=v[10]+1; else v[f]:=v[f]+1; fi;
   od;
od;
end:
P(10000);