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Leftmost 1 is converted to a 2, which then propagates one step at a time until it is rightmost; then it changes to a pair of 1's and the process repeats.
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%I #7 May 15 2018 14:34:13

%S 0,1,2,11,21,12,111,211,121,112,1111,2111,1211,1121,1112,11111,21111,

%T 12111,11211,11121,11112,111111,211111,121111,112111,111211,111121,

%U 111112,1111111,2111111,1211111,1121111,1112111,1111211,1111121,1111112

%N Leftmost 1 is converted to a 2, which then propagates one step at a time until it is rightmost; then it changes to a pair of 1's and the process repeats.

%C Arises in analysis of Bulgarian solitaire.

%H Harvey P. Dale, <a href="/A071762/b071762.txt">Table of n, a(n) for n = 0..1000</a>

%t f1[{a_,b_}]:={a,NestList[FromDigits[RotateRight[IntegerDigits[#]]]&, b, IntegerLength[ b]-1]}; Join[{0},f1/@Table[{FromDigits[PadRight[{},n,1]], FromDigits[ PadRight[{2},n,1]]},{n,7}]//Flatten] (* _Harvey P. Dale_, May 15 2018 *)

%Y Cf. A071761.

%K nonn,easy

%O 0,3

%A _Allan C. Wechsler_, Jun 07 2002

%E More terms from _Sascha Kurz_, Jan 28 2003