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

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, 54, 58, 62, 66, 70, 75, 80, 86, 92, 98, 104, 111, 118, 125, 132, 139, 146, 153, 160, 168, 176, 184, 192, 200, 210, 221, 232, 243, 254, 265, 276, 287, 298, 309, 321, 333, 345, 357, 369

Offset: 1

Author

Eric Angelini, Aug 05 2007

Keywords

• base
• easy
• nonn

Programs

Maple

A130232 := proc(n)
    option remember;
    if n = 1 then
        0;
    else
        a := procname(n-1) ;
        for j from 1 to n-1 do
            for d in convert(procname(j),base,10) do
                if d = 0 then
                    a := a+1 ;
                end if;
            end do:
        end do:
        a+1 ;
    end if;
end proc:
seq(A130232(n),n=1..80) ; # R. J. Mathar, Aug 06 2016

Mathematica

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 *)

Python

A130232_list, c = [0], 1
for _ in range(100):
    A130232_list.append(A130232_list[-1]+c)
    c += str(A130232_list[-1]).count('0') # Chai Wah Wu, Jun 06 2021

Extensions

Corrected by R. J. Mathar, Aug 06 2016