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A332113 a(n) = (10^(2n+1)-1)/9 + 2*10^n.

%I A332113 #10 Feb 11 2020 07:56:23
%S A332113 3,131,11311,1113111,111131111,11111311111,1111113111111,
%T A332113 111111131111111,11111111311111111,1111111113111111111,
%U A332113 111111111131111111111,11111111111311111111111,1111111111113111111111111,111111111111131111111111111,11111111111111311111111111111,1111111111111113111111111111111
%N A332113 a(n) = (10^(2n+1)-1)/9 + 2*10^n.
%C A332113 See A107123 = {0, 1, 2, 19, 97, 9818, ...} for the indices of primes.
%H A332113 Brady Haran and Simon Pampena, <a href="https://youtu.be/HPfAnX5blO0">Glitch Primes and Cyclops Numbers</a>, Numberphile video (2015).
%H A332113 Patrick De Geest, <a href="http://www.worldofnumbers.com/wing.htm#pwp131">Palindromic Wing Primes: (1)3(1)</a>, updated: June 25, 2017.
%H A332113 Makoto Kamada, <a href="https://stdkmd.net/nrr/1/11311.htm">Factorization of 11...11311...11</a>, updated Dec 11 2018.
%H A332113 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (111,-1110,1000).
%F A332113 a(n) = A138148(n) + 3*10^n = A002275(2n+1) + 2*10^n.
%F A332113 G.f.: (3 - 202*x + 100*x^2)/((1 - x)(1 - 10*x)(1 - 100*x)).
%F A332113 a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n > 2.
%p A332113 A332113 := n -> (10^(2*n+1)-1)/9+2*10^n;
%t A332113 Array[(10^(2 # + 1)-1)/9 + 2*10^# &, 15, 0]
%o A332113 (PARI) apply( {A332113(n)=10^(n*2+1)\9+2*10^n}, [0..15])
%o A332113 (Python) def A332113(n): return 10**(n*2+1)//9+2*10**n
%Y A332113 Cf. (A077779-1)/2 = A107123: indices of primes; A331864 & A331865 (non-palindromic variants).
%Y A332113 Cf. A002275 (repunits R_n = (10^n-1)/9), A011557 (10^n).
%Y A332113 Cf. A138148 (cyclops numbers with binary digits), A002113 (palindromes).
%Y A332113 Cf. A332123 .. A332193 (variants with different repeated digit 2, ..., 9).
%Y A332113 Cf. A332112 .. A332119 (variants with different middle digit 2, ..., 9).
%K A332113 nonn,base,easy
%O A332113 0,1
%A A332113 _M. F. Hasler_, Feb 09 2020