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A332194 a(n) = 10^(2n+1) - 1 - 5*10^n.

%I A332194 #13 Feb 11 2020 08:30:56
%S A332194 4,949,99499,9994999,999949999,99999499999,9999994999999,
%T A332194 999999949999999,99999999499999999,9999999994999999999,
%U A332194 999999999949999999999,99999999999499999999999,9999999999994999999999999,999999999999949999999999999,99999999999999499999999999999,9999999999999994999999999999999
%N A332194 a(n) = 10^(2n+1) - 1 - 5*10^n.
%C A332194 See A183185 = {14, 22, 36, 104, 1136, ...} for the indices of primes.
%H A332194 Patrick De Geest, <a href="http://www.worldofnumbers.com/wing.htm#pwp949">Palindromic Wing Primes: (9)4(9)</a>, updated Jun 25 2017.
%H A332194 Makoto Kamada, <a href="https://stdkmd.net/nrr/9/99499.htm">Factorization of 99...99499...99</a>, updated Dec 11 2018.
%H A332194 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (111,-1110,1000).
%F A332194 a(n) = 9*A138148(n) + 4*10^n = A002283(2n+1) - 5*A011557(n).
%F A332194 G.f.: (4 + 505*x - 1400*x^2)/((1 - x)*(1 - 10*x)*(1 - 100*x)).
%F A332194 a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n > 2.
%p A332194 A332194 := n -> 10^(n*2+1)-1-5*10^n;
%t A332194 Array[ 10^(2 # + 1) -1 -5*10^# &, 15, 0]
%o A332194 (PARI) apply( {A332194(n)=10^(n*2+1)-1-5*10^n}, [0..15])
%o A332194 (Python) def A332194(n): return 10**(n*2+1)-1-5*10^n
%Y A332194 Cf. (A077782-1)/2 = A183185: indices of primes.
%Y A332194 Cf. A002275 (repunits R_n = (10^n-1)/9), A002283 (9*R_n), A011557 (10^n).
%Y A332194 Cf. A138148 (cyclops numbers with binary digits only), A002113 (palindromes).
%Y A332194 Cf. A332114 .. A332184 (variants with different repeated digit 1, ..., 8).
%Y A332194 Cf. A332190 .. A332197, A181965 (variants with different middle digit 0, ..., 8).
%K A332194 nonn,base,easy
%O A332194 0,1
%A A332194 _M. F. Hasler_, Feb 08 2020