A357884 a(1)=0; if a(n-1) shares any digits with n-1, then a(n) = a(n-1) with all copies of digits from n-1 removed. Otherwise, a(n) = a(n-1) + (n-1).

0, 1, 3, 0, 4, 9, 15, 22, 30, 39, 49, 60, 72, 85, 99, 114, 4, 21, 2, 21, 1, 0, 22, 0, 24, 4, 30, 57, 85, 114, 144, 44, 76, 109, 143, 14, 50, 87, 7, 46, 6, 47, 7, 50, 94, 9, 55, 102, 150, 199, 249, 300, 352, 2, 56, 6, 0, 57, 7, 66, 0, 61, 1, 64, 0, 65, 5

Offset

1,3

Comments

If n-1 contains all digits of a(n-1), then a(n) = 0.

Links

Gavin Lupo, Table of n, a(n) for n = 1..10000

Thomas Scheuerle, Scatter plot log(1+a(1..100000))

Example

n                      a(n)
--                     ----
14                      85
15    85 + 14      =    99
16    99 + 15      =   114
17    1's removed  =     4

Mathematica

a[0] = 0; a[n_] := a[n] = Module[{da = IntegerDigits[a[n - 1]], dn = IntegerDigits[n - 1]}, If[Intersection[da, dn] == {}, a[n - 1] + n - 1, FromDigits[Select[da, ! MemberQ[dn, #] &]]]]; Array[a, 100, 0] (* Amiram Eldar, Oct 21 2022 *)

Prog

(MATLAB)
function a = A357884( max_n )
    a = 0;
    for n = 2:max_n
        sa = num2str(a(n-1));
        s = intersect(sa, num2str(n-2));
        if isempty(s)
            a(n) = a(n-1)+(n-2);
        else
            sd = ['0' regexprep(sa, ['[' s ']'], '')];
            a(n) = str2double(sd);
        end
    end
    a = a(2:end);
end % Thomas Scheuerle, Oct 18 2022
(Python)
from itertools import count, islice
def A357884_gen(): # generator of terms
    a, s = 0, '0'
    for n in count(1):
        yield a
        if len(t:=set(s)&set(str(n))) > 0:
            a = int(s.translate(s.maketrans('', '', ''.join(t))) or 0)
        else:
            a += n
        s = str(a)
A357884_list = list(islice(A357884_gen(), 30)) # Chai Wah Wu, Oct 27 2022

Crossrefs

Cf. A045541.

Sequence in context: A079406 A378505 A068627 * A074171 A180657 A375856

Adjacent sequences: A357881 A357882 A357883 * A357885 A357886 A357887

Keyword

nonn,base,easy,look

Author

Gavin Lupo, Oct 18 2022

Status

approved