Rhyming digits

[Eric Angelini]

Hello SeqFans,
is this seq worth the OEIS?

a(n) is always the smallest integer not yet present in S (="NYPIS")
and having its last digit equal to the n-st digit of S:

S = 1,11,21,2,31,12,3,41,51,22,51,32,13,4,...

a(1)= 1 is the smallest integer "NYPIS" ending with 1 (1st digit of S)
a(2)= 11 is the smallest integer ...    ending with 1 (2nd digit of S)
a(3)= 21 is the smallest integer ...    ending with 1 (3rd digit of S)
a(4)= 2 is the smallest integer ...     ending with 2 (4th digit of S)
a(5)= 31 is the smallest integer ...    ending with 1 (5th digit of S)
a(6)= 12 is the smallest integer ...    ending with 2 (6th digit of S)
a(7)= 3 is the smallest integer ...     ending with 3 (7th digit of S)
a(8)= 41 is the smallest integer ...    ending with 1 (8th digit of S)
...

Best,
É.

[Yes, one could start S in many different ways:
 S= 9,8,7,6,5,4,3,2,1, then 11,21,12,31,...
 S= 1,3,5,7,9,2,4,6,8, then 11,21,12,31,...
 S= 1,2,3,4,5,6,7,8,9, then 11,21,12,31,...]