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

1,1

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.

Links

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

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.

Example

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

Crossrefs

Cf. A284591, A285471, A285695.

Sequence in context: A267775 A267867 A267889 * A097580 A216786 A350320

Adjacent sequences: A285693 A285694 A285695 * A285697 A285698 A285699

Keyword

nonn,base

Author

Lars Blomberg and Eric Angelini, Apr 25 2017

Status

approved