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Start with a(0)=1; replace each i with 12...i, then add 1 to final digit.
1

%I #15 Mar 31 2017 22:51:27

%S 1,2,13,1124,11121235,1111211212312346,

%T 11111211121121231121231234123457,

%U 1111112111121112112123111211212311212312341121231234123451234568

%N Start with a(0)=1; replace each i with 12...i, then add 1 to final digit.

%H T. Kubo and R. Vakil, <a href="http://dx.doi.org/10.1016/0012-365X(94)00303-Z">On Conway's recursive sequence</a>, Discr. Math. 152 (1996), 225-252.

%H <a href="/index/Fi#final">Index entries for sequences related to final digits of numbers</a>

%K nonn,base

%O 0,2

%A _N. J. A. Sloane_