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 A332112 #8 Feb 11 2020 07:55:48
%S A332112 2,121,11211,1112111,111121111,11111211111,1111112111111,
%T A332112 111111121111111,11111111211111111,1111111112111111111,
%U A332112 111111111121111111111,11111111111211111111111,1111111111112111111111111,111111111111121111111111111,11111111111111211111111111111,1111111111111112111111111111111
%N A332112 a(n) = (10^(2n+1)-1)/9 + 10^n.
%C A332112 a(0) = 2 is the only prime in this sequence, since all other terms factor as a(n) = R(n+1)*(10^n+1), where R(n) = (10^n-1)/9.
%H A332112 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (111,-1110,1000).
%F A332112 a(n) = A138148(n) + 2*10^n = A002275(2n+1) + 10^n.
%F A332112 G.f.: (2 - 101*x)/((1 - x)(1 - 10*x)(1 - 100*x)).
%F A332112 a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n > 2.
%p A332112 A332112 := n -> (10^(2*n+1)-1)/9+10^n;
%t A332112 Array[ (10^(2 # + 1)-1)/9 + 10^# &, 15, 0]
%o A332112 (PARI) apply( {A332112(n)=10^(n*2+1)\9*1+10^n}, [0..15])
%o A332112 (Python) def A332112(n): return 10**(n*2+1)//9+10**n
%Y A332112 Cf. A002275 (repunits R_n = (10^n-1)/9), A011557 (10^n).
%Y A332112 Cf. A138148 (cyclops numbers with binary digits), A002113 (palindromes).
%Y A332112 Cf. A332132 .. A332192 (variants with different repeated digit 3, ..., 9).
%Y A332112 Cf. A332113 .. A332119 (variants with different middle digit 3, ..., 9).
%Y A332112 Cf. A331860 & A331861 (indices of primes in non-palindromic variants).
%K A332112 nonn,base,easy
%O A332112 0,1
%A A332112 _M. F. Hasler_, Feb 09 2020