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A130224 a(1) = 1; a(n) = a(n-1) + (number of times the digit 1 has appeared in the sequence so far).

%I A130224 #13 Feb 08 2025 11:23:41
%S A130224 1,2,3,4,5,6,7,8,9,10,12,15,19,24,29,34,39,44,49,54,59,64,69,74,79,84,
%T A130224 89,94,99,104,110,118,128,139,151,165,180,196,213,231,250,269,288,307,
%U A130224 326,345,364,383,402,421,441,462
%N A130224 a(1) = 1; a(n) = a(n-1) + (number of times the digit 1 has appeared in the sequence so far).
%H A130224 Michael De Vlieger, <a href="/A130224/b130224.txt">Table of n, a(n) for n = 1..10000</a>
%p A130224 A130224 := proc(n)
%p A130224     option remember;
%p A130224     if n = 1 then
%p A130224         1;
%p A130224     else
%p A130224         a := procname(n-1) ;
%p A130224         for j from 1 to n-1 do
%p A130224             for d in convert(procname(j),base,10) do
%p A130224                 if d = 1 then
%p A130224                     a := a+1 ;
%p A130224                 end if;
%p A130224             end do:
%p A130224         end do:
%p A130224         a ;
%p A130224     end if;
%p A130224 end proc:
%p A130224 seq(A130224(n),n=1..52) ; # _R. J. Mathar_, Aug 06 2016
%t A130224 ss={1};s={1};Do[a=ss[[-1]]+Count[s,1];s=Join[s,IntegerDigits[a]];AppendTo[ss,a],{n,2,52}];ss (* _James C. McMahon_, Feb 08 2025 *)
%K A130224 base,easy,nonn
%O A130224 1,2
%A A130224 _Eric Angelini_, Aug 05 2007