Jelly, 4 bytes

Since xnor came up with this algorithm, I will make this community wiki.

Bṙ1Ḅ

Try it online!

Explanation

Bṙ1Ḅ
B convert to binary
 ṙ1 left-rotate by 1
 Ḅ convert from binary

Jelly, 4 bytes

Since xnor came up with this algorithm, I will make this community wiki.

Bṙ1Ḅ

Try it online!

Explanation

Bṙ1Ḅ
B convert to binary
 ṙ1 left-rotate by 1
 Ḅ convert from binary

Jelly, (削除) 4 (削除ここまで) 3 bytes

_{Crossed out 4 is still regular 4 ;(}

Since xnor came up with this algorithm, I will make this community wiki.

(削除) Bṙ1Ḅ (削除ここまで)
&Ḥ‘

Try it online!

Explanation

Bṙ1Ḅ
B convert to binary
 ṙ1 left-rotate by 1
 Ḅ convert from binary
&Ḥ‘
&Ḥ z and (z*2)
 ‘ +1

Jelly, 4 bytes

Since xnor came up with this algorithm, I will make this community wiki.

Bṙ1Ḅ

Try it online!

Explanation

Bṙ1Ḅ
B convert to binary
 ṙ1 left-rotate by 1
 Ḅ convert from binary