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A068168 Define an increasing sequence as follows. Given the first term called the seed (the seed need not have the property of the sequence.). Subsequent terms are defined as obtained by inserting/placing digits (at least one) in the previous term to obtain the smallest number with a given property. This is the growing prime sequence for the seed a(1) = 3.

%I A068168 #8 Nov 07 2014 17:12:06
%S A068168 3,13,103,1013,10103,100103,1001003,10010023,100010023,1000100239,
%T A068168 10001000239,100010002039,1000100020319,10001000200319,
%U A068168 100001000200319,1000010002000319,10000100002000319,100001000020003109,1000010000200031039,10000100002000310329
%N A068168 Define an increasing sequence as follows. Given the first term called the seed (the seed need not have the property of the sequence.). Subsequent terms are defined as obtained by inserting/placing digits (at least one) in the previous term to obtain the smallest number with a given property. This is the growing prime sequence for the seed a(1) = 3.
%C A068168 a(5) onwards the sequence is A068166.
%H A068168 Alois P. Heinz, <a href="/A068168/b068168.txt">Table of n, a(n) for n = 1..300</a>
%e A068168 The primes obtained by inserting/placing a digit in a(2) = 13 are 113,131,313 etc... a(3)= 113 is the smallest.
%p A068168 a:= proc(n) option remember; local s, w, m;
%p A068168       if n=1 then 3
%p A068168     else w:=a(n-1); s:=""||w; m:=length(s);
%p A068168          min(select(x->length(x)=m+1 and isprime(x),
%p A068168          {seq(seq(parse(cat(seq(s[h], h=1..i), j,
%p A068168          seq(s[h], h=i+1..m))), j=0..9), i=0..m)})[])
%p A068168       fi
%p A068168     end:
%p A068168 seq(a(n), n=1..23);  # _Alois P. Heinz_, Nov 07 2014
%Y A068168 Cf. A068166, A068167.
%K A068168 base,nonn
%O A068168 1,1
%A A068168 _Amarnath Murthy_, Feb 25 2002
%E A068168 Corrected and extended by _Robert Gerbicz_, Sep 06 2002