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a(n)=Sum_digits_of_a(n-1)+Sum_digits_of(n).
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%I #7 Feb 02 2017 10:54:17

%S 0,1,3,6,10,6,12,10,9,18,10,3,6,10,6,12,10,9,18,19,12,6,10,6,12,10,9,

%T 18,19,21,6,10,6,12,10,9,18,19,21,15,10,6,12,10,9,18,19,21,15,19,15,

%U 12,10,9,18,19,21,15,19,24,12,10,9,18,19,21,15,19,24,21,10,9,18,19,21,15,19

%N a(n)=Sum_digits_of_a(n-1)+Sum_digits_of(n).

%H Harvey P. Dale, <a href="/A139762/b139762.txt">Table of n, a(n) for n = 0..1000</a>

%p P:=proc(n) local a,i,k,w,x; a:=0; print(a); for i from 1 by 1 to n do w:=0; k:=i; while k>0 do w:=w+k-(trunc(k/10)*10); k:=trunc(k/10); od; x:=0; k:=a; while k>0 do x:=x+k-(trunc(k/10)*10); k:=trunc(k/10); od; a:=w+x; print(a); od; end: P(101);

%t nxt[{n_,a_}]:={n+1,Total[IntegerDigits[a]]+Total[IntegerDigits[n+1]]}; NestList[nxt,{0,0},80][[All,2]] (* _Harvey P. Dale_, Feb 02 2017 *)

%K easy,nonn

%O 0,3

%A _Paolo P. Lava_ and _Giorgio Balzarotti_, May 20 2008