cp's OEIS Frontend

A289351 Starting from one digit move right by x steps, x being the value of the digit. If the steps go beyond the least significant digits they continue from the left side. Then repeat the process from the reached digit. The sequence lists the numbers such that all the digits are touched just one time and the last run ends in the initial digit.

%I A289351 #22 Sep 08 2023 22:37:18
%S A289351 0,1,2,3,4,5,6,7,8,9,11,13,15,17,19,31,33,35,37,39,51,53,55,57,59,71,
%T A289351 73,75,77,79,91,93,95,97,99,111,114,117,141,144,147,171,174,177,222,
%U A289351 225,228,252,255,258,282,285,288,411,414,417,441,444,447,471,474,477
%N A289351 Starting from one digit move right by x steps, x being the value of the digit. If the steps go beyond the least significant digits they continue from the left side. Then repeat the process from the reached digit. The sequence lists the numbers such that all the digits are touched just one time and the last run ends in the initial digit.
%C A289351 Apart from a(0), only zeroless numbers.
%C A289351 If we move left instead of right, the sequence is the same up to a(103); here, a(103)=1223 while in the other sequence a(103) would be 1322.
%H A289351 Paolo P. Lava, <a href="/A289351/b289351.txt">Table of n, a(n) for n = 0..10000</a>
%e A289351 13894: for instance, let us start from 8. Moving eight steps right we are at 1. Then, moving one step right we are at 3. Then 3 steps right we are at 4. Again after 4 steps we are at 9. After an additional 9 steps we end at 8 again. All the digits have been touched and we are again at the digit we started from.
%p A289351 P:=proc(q) local a,b,d,k,n,t; print(0); for n from 1 to q do d:=ilog10(n)+1; a:=convert(n,base,10);
%p A289351 for k from 1 to trunc(d/2) do b:=a[k]; a[k]:=a[d-k+1]; a[d-k+1]:=b; od; b:=array(1..d);
%p A289351 for k from 1 to d do b[k]:=0; od; t:=1; for k from 1 to d do
%p A289351 if ((t+(a[t] mod d)) mod d)>0 then b[(t+(a[t] mod d)) mod d]:=1; t:=(t+(a[t] mod d)) mod d;
%p A289351 else b[d]:=1; t:=d; fi; od; if add(b[k],k=1..d)=d then print(n); fi; od; end: P(10^9);
%t A289351 Select[Range[0,477],(n=IntegerDigits@#;Last[m=Mod[Accumulate@Mod[n,s=Length@n],s]]==0&&Sort@m+1==Range@s)&] (* _Giorgos Kalogeropoulos_, Nov 21 2021 *)
%Y A289351 Cf. A014261 (2 digits terms), A071073 (3 digits terms up to 588), A284515, A284591.
%K A289351 nonn,base,easy
%O A289351 0,3
%A A289351 _Paolo P. Lava_, Jul 03 2017