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

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

Author

Lars Blomberg and Eric Angelini, Apr 25 2017

Keywords

• nonn
• base

Comments

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.

Examples

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

Links

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

Crossrefs

Cf. A284591, A285471, A285695.

Formula

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.