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).

%I A284591 #39 Mar 09 2025 06:28:33
%S A284591 100,1102,11122,30000,111124,130200,300102,330004,1031202,1111144,
%T A284591 1132200,1302102,1332004,3001122,3031024,3102120,3130240,3300142,
%U A284591 3330044,3332222,5000000,5011222,5112220,5310242,5312024,10110140,10312122,11031402,11111146,11132400,11322102,11332006,13021122,13031026,13122120,13130440
%N 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).
%C A284591 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".
%H A284591 Lars Blomberg, <a href="/A284591/b284591.txt">Table of n, a(n) for n = 1..10000</a> (The first 544 terms from Jean-Marc Falcoz)
%e A284591 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.)
%Y A284591 Cf. A284515, A285471, A285695, A285696
%K A284591 nonn,base
%O A284591 1,1
%A A284591 _Eric Angelini_ and _Jean-Marc Falcoz_, Mar 29 2017 and Mar 30 2017