

A289351


Starting from one digit move right by x steps, being x the value of the digit. If the steps go beyond the LSD 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 end in the initial digit.


1



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, 73, 75, 77, 79, 91, 93, 95, 97, 99, 111, 114, 117, 141, 144, 147, 171, 174, 177, 222, 225, 228, 252, 255, 258, 282, 285, 288, 411, 414, 417, 441, 444, 447, 471, 474, 477
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OFFSET

0,3


COMMENTS

Apart from a(0), only zeroless numbers.
If instead of moving right we move left the sequence is equal up to a(103).
Here is a(103)=1223 while in the other sequence would be a(103)=1322.


LINKS

Paolo P. Lava, Table of n, a(n) for n = 0..10000


EXAMPLE

13894: for instance, let us start from 8. The reached positions are:
Step Position
1 9
2 4
3 1
4 3
5 8
6 9
7 4
8 1
Now we are in digit 1. Moving one step right we are in 3. Then 3 steps right we are in 4. Again after 4 steps we are in 9. After additional 9 steps we end in 8 again. All the digits have been touched and we are again in the digit we started from.


MAPLE

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);
for k from 1 to trunc(d/2) do b:=a[k]; a[k]:=a[dk+1]; a[dk+1]:=b; od; b:=array(1..d);
for k from 1 to d do b[k]:=0; od; t:=1; for k from 1 to d do
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;
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);


CROSSREFS

Cf. A014261 (2 digits terms), A071073 (3 digits terms up to 588), A284515, A284591.
Sequence in context: A088450 A279080 A108641 * A171550 A062895 A085869
Adjacent sequences: A289348 A289349 A289350 * A289352 A289353 A289354


KEYWORD

nonn,base,easy


AUTHOR

Paolo P. Lava, Jul 03 2017


STATUS

approved



