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A130232 a(1) = 0; a(n) = a(n-1) + (number of times the digit 0 has appeared in the sequence so far).

%I A130232 #14 Feb 08 2025 16:04:59
%S A130232 0,1,2,3,4,5,6,7,8,9,10,12,14,16,18,20,23,26,29,32,35,38,41,44,47,50,
%T A130232 54,58,62,66,70,75,80,86,92,98,104,111,118,125,132,139,146,153,160,
%U A130232 168,176,184,192,200,210,221,232,243,254,265,276,287,298,309,321,333,345,357,369
%N A130232 a(1) = 0; a(n) = a(n-1) + (number of times the digit 0 has appeared in the sequence so far).
%p A130232 A130232 := proc(n)
%p A130232     option remember;
%p A130232     if n = 1 then
%p A130232         0;
%p A130232     else
%p A130232         a := procname(n-1) ;
%p A130232         for j from 1 to n-1 do
%p A130232             for d in convert(procname(j),base,10) do
%p A130232                 if d = 0 then
%p A130232                     a := a+1 ;
%p A130232                 end if;
%p A130232             end do:
%p A130232         end do:
%p A130232         a+1 ;
%p A130232     end if;
%p A130232 end proc:
%p A130232 seq(A130232(n),n=1..80) ; # _R. J. Mathar_, Aug 06 2016
%t A130232 ss=s={0};Do[a=ss[[-1]]+Count[s,0];s=Join[s,IntegerDigits[a]];AppendTo[ss,a],{n,64}];ss (* _James C. McMahon_, Feb 08 2025 *)
%o A130232 (Python)
%o A130232 A130232_list, c = [0], 1
%o A130232 for _ in range(100):
%o A130232     A130232_list.append(A130232_list[-1]+c)
%o A130232     c += str(A130232_list[-1]).count('0') # _Chai Wah Wu_, Jun 06 2021
%K A130232 base,easy,nonn
%O A130232 1,3
%A A130232 _Eric Angelini_, Aug 05 2007
%E A130232 Corrected by _R. J. Mathar_, Aug 06 2016