A285695 -id:A285695 - 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

A285696 Numbers such that the path described in Comments visits all digits once and ends in the position immediately after the last digit.

Original entry on oeis.org

110, 11112, 33000, 110110, 313122, 1111114, 1133200, 1303102, 1333004, 1531202, 3103120, 3130210, 3300112, 3330014, 3333222, 3501122, 3531024, 5113220, 5310212, 5313024, 5500000, 5511222, 11011112, 11033000, 11112110, 11313142, 13030010, 15013020, 31312114

Offset: 1

Lars Blomberg and Eric Angelini, Apr 25 2017

Let d(1..k) be the digits in the number and let i = 1. If d(i) is odd set i = i+d(i)+1 else i = i-d(i)-1. The number is a term if i reaches k+1.

			For 33000 the digit positions visited are 1, 5, 4, 3, 2, 6(outside to the right) so 33000 is a term.

Lars Blomberg, Table of n, a(n) for n = 1..10000

Cf. A284591, A285471, A285695.

Numbers must start with 1, 3, 5, 7, 9 and end with 0, 2, 4, 6, 8.

Let eSum = Sum_{i=1..k, d(i) is even} d(i)+1, and oSum = Sum_{i=1..k, d(i) is odd} d(i)+1. Then eSum-oSum+k = 0.

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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