A285695 Numbers such that the path described in Comments visits all digits once and ends in the position before the first digit.

0, 31202, 110140, 312122, 1101106, 1131404, 3121124, 3131226, 5111424, 5120200, 5300402, 5320004, 11011162, 11034000, 11112160, 11314142, 13030060, 15014020, 31211144, 31232200, 31312164, 33000160, 33202120, 33230240, 35010260, 35212220, 51034202, 51114144

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 0.

Examples

			For 31202 the digit positions visited are 1, 5, 2, 4, 3, 0(outside to the left) so 31202 is a term.
		

Links

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

Crossrefs

Cf. A284591, A285471, A285696.

Formula

Except for 0, 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-1 = 0.