A284515 -id:A284515 - cp's OEIS frontend

A284591 "Full Inside numbers". Such numbers have the property that all their digits will be visited exactly once in a single closed circuit (see Comments).

100, 1102, 11122, 30000, 111124, 130200, 300102, 330004, 1031202, 1111144, 1132200, 1302102, 1332004, 3001122, 3031024, 3102120, 3130240, 3300142, 3330044, 3332222, 5000000, 5011222, 5112220, 5310242, 5312024, 10110140, 10312122, 11031402, 11111146, 11132400, 11322102, 11332006, 13021122, 13031026, 13122120, 13130440

Offset: 1

Eric Angelini and Jean-Marc Falcoz, Mar 29 2017 and Mar 30 2017

The sequence is started with a(1) = 100 and always extended with the smallest integer not yet present and not leading to a contradiction. See A284515 for the definition of an "Inside number".

			The 13th term of the sequence is 1332004. This integer is in the sequence because starting on the first digit "1", will lead to the second "3" (after jumping over exactly one digit to the right), then to "4" (after jumping exactly over three digits to the right), then to the first "3" (after jumping exactly over four digits to the left), then to the last "0" (after jumping exactly over three digits to the right), then to the first "0" (after jumping exactly over no digit to the left, which is equivalent to "sliding" to the digit on the left), then to "2" (same reason), then to the initial "1" (after jumping exactly over two digits to the left). The cycle has come to its end. (The direction -left or right- of a jump is given by the parity -odd or even- of the digit involved.)

Lars Blomberg, Table of n, a(n) for n = 1..10000 (The first 544 terms from Jean-Marc Falcoz)

Cf. A284515, A285471, A285695, A285696

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.

Original entry on oeis.org

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

Offset: 0

Paolo P. Lava, Jul 03 2017

Apart from a(0), only zeroless numbers.

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.

			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.

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

Cf. A014261 (2 digits terms), A071073 (3 digits terms up to 588), A284515, A284591.

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[d-k+1]; a[d-k+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);

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 *)

cp's OEIS Frontend

A284591 "Full Inside numbers". Such numbers have the property that all their digits will be visited exactly once in a single closed circuit (see Comments).

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