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

1,2

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.

Links

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

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.

Example

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

Crossrefs

Cf. A284591, A285471, A285696.

Sequence in context: A234888 A151815 A331675 * A186800 A230753 A205419

Adjacent sequences: A285692 A285693 A285694 * A285696 A285697 A285698

Keyword

nonn,base

Author

Lars Blomberg and Eric Angelini, Apr 25 2017

Status

approved