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A068167 Define an increasing sequence as follows. Given the first term, called the seed (which need not share the property of the remaining terms), subsequent terms are obtained by inserting at least one digit in the previous term so as to obtain the smallest number with the specified property. This is the prime sequence with the seed a(1) = 2.

%I A068167 #19 Sep 13 2015 04:59:20
%S A068167 2,23,223,1223,10223,102023,1020023,10200263,102002603,1020026303,
%T A068167 10200226303,102002263031,1020002263031,10200022363031,
%U A068167 102000223263031,1020000223263031,10200002232630131,102000022326301313,1020000222326301313,10200002223236301313
%N A068167 Define an increasing sequence as follows. Given the first term, called the seed (which need not share the property of the remaining terms), subsequent terms are obtained by inserting at least one digit in the previous term so as to obtain the smallest number with the specified property. This is the prime sequence with the seed a(1) = 2.
%H A068167 Alois P. Heinz, <a href="/A068167/b068167.txt">Table of n, a(n) for n = 1..300</a>
%e A068167 The primes that can be obtained by inserting/placing a digit in a(2) = 23 are 223, 233, 239, 263, 283, 293, etc. a(3) = 223 is the smallest.
%p A068167 a:= proc(n) option remember; local s, w, m;
%p A068167       if n=1 then 2
%p A068167     else w:=a(n-1); s:=""||w; m:=length(s);
%p A068167          min(select(x->length(x)=m+1 and isprime(x),
%p A068167          {seq(seq(parse(cat(seq(s[h], h=1..i), j,
%p A068167          seq(s[h], h=i+1..m))), j=0..9), i=0..m)})[])
%p A068167       fi
%p A068167     end:
%p A068167 seq(a(n), n=1..23);  # _Alois P. Heinz_, Nov 07 2014
%Y A068167 Cf. A068166, A030456.
%K A068167 base,nonn
%O A068167 1,1
%A A068167 _Amarnath Murthy_, Feb 25 2002
%E A068167 Corrected and extended by _Robert Gerbicz_, Sep 06 2002