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A048553 a(n+1) is next smallest prime beginning with a(n), initial prime is 11.

%I A048553 #17 Sep 30 2015 08:53:44
%S A048553 11,113,11311,113111,1131113,11311133,1131113353,113111335313,
%T A048553 11311133531339,113111335313399,1131113353133993,113111335313399321,
%U A048553 11311133531339932153,1131113353133993215379,113111335313399321537911
%N A048553 a(n+1) is next smallest prime beginning with a(n), initial prime is 11.
%H A048553 Clark Kimberling, <a href="/A048553/b048553.txt">Table of n, a(n) for n = 0..498</a>
%p A048553 f:= proc(n)
%p A048553   local p, d;
%p A048553   for d from 1 do
%p A048553     p:= nextprime(n*10^d);
%p A048553     if p < (n+1)*10^d then return p fi
%p A048553   od
%p A048553 end proc:
%p A048553 A[1]:= 11:
%p A048553 for n from 2 to 20 do A[n]:= f(A[n-1]) od:
%p A048553 seq(A[n], n=1..20); # _Robert Israel_, Aug 16 2015
%t A048553 a = {11}; Do[k = 1; w = IntegerDigits[a[[n - 1]]];
%t A048553 While[CompositeQ@ FromDigits[Join[w, IntegerDigits@ k]], k += 2];
%t A048553 AppendTo[a, FromDigits[Join[w, IntegerDigits@ k]]], {n, 2, 15}]; a (* _Michael De Vlieger_, Sep 21 2015 *)
%Y A048553 Cf. A048549-A048556, A261199-A261201, A261269-A261270.
%K A048553 nonn,base
%O A048553 0,1
%A A048553 _Patrick De Geest_, May 15 1999