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A332197 a(n) = 10^(2n+1) - 1 - 2*10^n.

%I A332197 #17 May 02 2024 22:54:48
%S A332197 7,979,99799,9997999,999979999,99999799999,9999997999999,
%T A332197 999999979999999,99999999799999999,9999999997999999999,
%U A332197 999999999979999999999,99999999999799999999999,9999999999997999999999999,999999999999979999999999999,99999999999999799999999999999,9999999999999997999999999999999
%N A332197 a(n) = 10^(2n+1) - 1 - 2*10^n.
%C A332197 According to Kamada, n = 118 and n = 145126 are the only known indices of primes (the so-called palindromic near-repdigit or wing primes).
%H A332197 Patrick De Geest, <a href="http://www.worldofnumbers.com/wing.htm#pwp979">Palindromic Wing Primes: (9)7(9)</a>, updated June 25, 2017.
%H A332197 Makoto Kamada, <a href="https://stdkmd.net/nrr/9/99799.htm">Factorization of 99...99799...99</a>, updated Dec 11 2018.
%H A332197 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (111,-1110,1000).
%F A332197 a(n) = 9*A138148(n) + 7*10^n.
%F A332197 G.f.: (7 + 202*x - 1100*x^2)/((1 - x)*(1 - 10*x)*(1 - 100*x)).
%F A332197 a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n > 2.
%p A332197 A332197 := n -> 10^(n*2+1)-1-2*10^n;
%t A332197 Array[ 10^(2 # + 1) -1 -2*10^# &, 15, 0]
%t A332197 Table[FromDigits[Join[PadRight[{},n,9],{7},PadRight[{},n,9]]],{n,0,20}] (* or *) LinearRecurrence[{111,-1110,1000},{7,979,99799},20] (* _Harvey P. Dale_, Mar 03 2023 *)
%o A332197 (PARI) apply( {A332197(n)=10^(n*2+1)-1-2*10^n}, [0..15])
%o A332197 (Python) def A332197(n): return 10**(n*2+1)-1-2*10^n
%Y A332197 Cf. A002275 (repunits R_n = (10^n-1)/9), A002283 (9*R_n), A011557 (10^n).
%Y A332197 Cf. A138148 (cyclops numbers with binary digits only).
%Y A332197 Cf. A332190 .. A332196, A181965 (variants with different middle digit 0, ..., 8).
%Y A332197 Cf. A332117 .. A332187 (variants with different repeated digit 1, ..., 9).
%K A332197 nonn,base,easy
%O A332197 0,1
%A A332197 _M. F. Hasler_, Feb 08 2020