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

1,2

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

Example

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.

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);

Crossrefs

Cf. A045918, A063850, A138484-A138493

Sequence in context: A215427 A139019 A031869 * A045360 A001915 A127437

Adjacent sequences: A194851 A194852 A194853 * A194855 A194856 A194857

Keyword

nonn,base

Author

Paolo P. Lava, Sep 07 2011

Status

approved