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 A080442 #15 Dec 23 2021 02:24:53
%S A080442 19,109,10009,100000039,10000000000002359,
%T A080442 100000000000000000000000002031519,
%U A080442 10000000000000000000000000000000000000000000000000002000301050179
%N A080442 a(1) = 19, a(n) is the smallest prime obtained by inserting digits between every pair of digits of a(n-1).
%C A080442 Conjecture: Only one digit needs to be inserted between each pair of digit of a(n-1) to get a(n); i.e., a(n) contains exactly 2n-1 digits for n > 1.
%C A080442 The conjecture above is false: a(5) = 10000000000002359 has 17 digits instead of 2*5 - 1 = 9. A refined conjecture is: a(n) contains exactly 2^(n-1) + 1 digits for all n > 0. This follows trivially from the initial conjecture of only one digit needed between each pair, and the fact that we start with 19, a 2-digit number, and holds true at least till a(12). - _Julio Cesar Hernandez-Castro_, Jul 07 2011
%H A080442 Julio Cesar Hernandez-Castro, <a href="/A080442/b080442.txt">Table of n, a(n) for n = 1..12</a>
%t A080442 a[n_] := Block[{d = IntegerDigits[n]}, k = Length[d]; While[k > 1, d = Insert[d, 0, k]; k-- ]; d = FromDigits[d]; e = d; k = 0; While[ !PrimeQ[e], k++; e = d + 10FromDigits[ IntegerDigits[k], 100]]; e]; NestList[a, 19, 6]
%Y A080442 Cf. A080439, A080440, A080441, A080883 - A080914.
%K A080442 base,nonn
%O A080442 1,1
%A A080442 _Amarnath Murthy_, Feb 22 2003
%E A080442 Edited and extended by _Robert G. Wilson v_, Feb 22 2003