This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A068174 #19 Aug 01 2022 18:24:23
%S A068174 9,19,109,1009,10009,100019,1000159,10001569,100001569,1000015069,
%T A068174 10000135069,100001350649,1000013500649,10000130500649,
%U A068174 100001303500649,1000013032500649,10000103032500649,100001030325003649,1000010130325003649,10000101303250036493
%N A068174 Define an increasing sequence as follows. Start with an initial term, the seed (which need not have the property of the sequence); subsequent terms are obtained by inserting/placing at least one digit in the previous term to obtain the smallest number with the given property. This is the prime sequence with the seed a(1) = 9.
%H A068174 Alois P. Heinz, <a href="/A068174/b068174.txt">Table of n, a(n) for n = 1..300</a>
%e A068174 The primes obtained by inserting/placing a digit in a(2) = 19 are 109, 139, 149, 179, 199 etc. and a(3) = 109 is the smallest.
%t A068174 f[n_] := Block[{b = PadLeft[ IntegerDigits[n], Floor[ Log[10, n] + 1]], k = 0}, While[ !PrimeQ[ FromDigits[ Insert[b, k, -2]]], k++ ]; FromDigits[ Insert[b, k, -2]]]; NestList[ f, 9, 18]
%Y A068174 Cf. A068166, A068167, A068169, A068170, A068171, A068172, A068173.
%K A068174 base,nonn
%O A068174 1,1
%A A068174 _Amarnath Murthy_, Feb 25 2002
%E A068174 Edited by _N. J. A. Sloane_ and _Robert G. Wilson v_, May 08 2002
%E A068174 Corrected and extended by _Robert Gerbicz_, Sep 06 2002