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A332195 a(n) = 10^(2n+1) - 4*10^n - 1.

%I A332195 #12 Feb 11 2020 08:32:34
%S A332195 5,959,99599,9995999,999959999,99999599999,9999995999999,
%T A332195 999999959999999,99999999599999999,9999999995999999999,
%U A332195 999999999959999999999,99999999999599999999999,9999999999995999999999999,999999999999959999999999999,99999999999999599999999999999,9999999999999995999999999999999
%N A332195 a(n) = 10^(2n+1) - 4*10^n - 1.
%C A332195 See A183186 = {88, 112, 198, 622, 4228, ...} for the indices of primes.
%H A332195 Patrick De Geest, <a href="http://www.worldofnumbers.com/wing.htm#pwp959">Palindromic Wing Primes: (9)5(9)</a>, updated Jun 25 2017.
%H A332195 Makoto Kamada, <a href="https://stdkmd.net/nrr/9/99599.htm">Factorization of 99...99599...99</a>, updated Dec 11 2018.
%H A332195 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (111,-1110,1000).
%F A332195 a(n) = 9*A138148(n) + 5*10^n.
%F A332195 G.f.: (5 + 404*x - 1300*x^2)/((1 - x)(1 - 10*x)(1 - 100*x)).
%F A332195 a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n > 2.
%p A332195 A332195 := n -> 10^(n*2+1)-4*10^n-1;
%t A332195 Array[ 10^(2 # + 1) - 1 - 4*10^# &, 15, 0]
%o A332195 (PARI) apply( {A332195(n)=10^(n*2+1)-1-4*10^n}, [0..15])
%o A332195 (Python) def A332195(n): return 10**(n*2+1)-1-4*10^n
%Y A332195 Cf. (A077786-1)/2 = A183186: indices of primes.
%Y A332195 Cf. A002275 (repunits R_n = (10^n-1)/9), A002283 (9*R_n), A011557 (10^n).
%Y A332195 Cf. A138148 (cyclops numbers with binary digits only), A002113 (palindromes).
%Y A332195 Cf. A332115 .. A332185 (variants with different repeated digit 1, ..., 8).
%Y A332195 Cf. A332190 .. A332197, A181965 (variants with different middle digit 0, ..., 8).
%K A332195 nonn,base,easy
%O A332195 0,1
%A A332195 _M. F. Hasler_, Feb 08 2020