A357884 - OEIS

%I #43 Oct 29 2022 07:06:31

%S 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,

%T 30,57,85,114,144,44,76,109,143,14,50,87,7,46,6,47,7,50,94,9,55,102,

%U 150,199,249,300,352,2,56,6,0,57,7,66,0,61,1,64,0,65,5

%N 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).

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

%H Gavin Lupo, <a href="/A357884/b357884.txt">Table of n, a(n) for n = 1..10000</a>

%H Thomas Scheuerle, <a href="/A357884/a357884.png">Scatter plot log(1+a(1..100000))</a>

%e n                      a(n)

%e --                     ----

%e 14                      85

%e 15    85 + 14      =    99

%e 16    99 + 15      =   114

%e 17    1's removed  =     4

%t 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 *)

%o (MATLAB)

%o function a = A357884( max_n )

%o     a = 0;

%o     for n = 2:max_n

%o         sa = num2str(a(n-1));

%o         s = intersect(sa,num2str(n-2));

%o         if isempty(s)

%o             a(n) = a(n-1)+(n-2);

%o         else

%o             sd = ['0' regexprep(sa,['[' s ']'],'')];

%o             a(n) = str2double(sd);

%o         end

%o     end

%o     a = a(2:end);

%o end % _Thomas Scheuerle_, Oct 18 2022

%o (Python)

%o from itertools import count, islice

%o def A357884_gen(): # generator of terms

%o     a, s = 0, '0'

%o     for n in count(1):

%o         yield a

%o         if len(t:=set(s)&set(str(n))) > 0:

%o             a = int(s.translate(s.maketrans('','',''.join(t))) or 0)

%o         else:

%o             a += n

%o         s = str(a)

%o A357884_list = list(islice(A357884_gen(),30)) # _Chai Wah Wu_, Oct 27 2022

%Y Cf. A045541.

%K nonn,base,easy,look

%O 1,3

%A _Gavin Lupo_, Oct 18 2022