[seqfan] Re: a(n) = a(n-1) + [sum of all digits present so far]

[Alois Heinz]

Eric Angelini schrieb:
> Hello SeqFans,
> this seems not to be in the OEIS (else I need new glasses):
>
> S = 1, 2, 5, 13, 25, 44, 71, 106, 113, ...
>
> a(1) = 1
> a(n) = a(n-1) + [sum of all digits present so far in S]
>
> (thus 25 = 13 + 1 + 2 + 5 + 1 + 3)
so you mean sum of decimal digits ...

  1, 2, 5, 13, 25, 44, 71, 106, 148, 203, 263, 334, 415,
  506, 608, 724, 853, 998, 1169, 1357, 1561, 1778, 2018,
  2269, 2539, 2828, 3137, 3460, 3796, 4157, 4535, 4930,
  5341, 5765, 6212, 6670, 7147, 7643, 8159, 8698, 9268,
  9863, 10484, 11122, 11767, 12434, 13115, 13807, 14518,
  15248

b:= proc(n) option remember; local m;
   m:= a(n);
   `if` (n=1, 0, b(n-1));
   while m>0 do
     %+ irem (m, 10, 'm')
   od;
   %
end;
a:= proc(n) option remember;
  `if` (n=1, 1, a(n-1) +b(n-1))
end;
seq (a(n), n=1..50);


Alois