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A332192 a(n) = 10^(2n+1) - 1 - 7*10^n.

%I A332192 #13 Nov 07 2022 12:52:34
%S A332192 2,929,99299,9992999,999929999,99999299999,9999992999999,
%T A332192 999999929999999,99999999299999999,9999999992999999999,
%U A332192 999999999929999999999,99999999999299999999999,9999999999992999999999999,999999999999929999999999999,99999999999999299999999999999,9999999999999992999999999999999
%N A332192 a(n) = 10^(2n+1) - 1 - 7*10^n.
%C A332192 See A115073 = {1, 8, 9, 352, 530, 697, ...} for the indices of primes.
%H A332192 Patrick De Geest, <a href="http://www.worldofnumbers.com/wing.htm#pwp929">Palindromic Wing Primes: (9)2(9)</a>, updated: June 25, 2017.
%H A332192 Makoto Kamada, <a href="https://stdkmd.net/nrr/9/99299.htm">Factorization of 99...99299...99</a>, updated Dec 11 2018.
%H A332192 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (111,-1110,1000).
%F A332192 a(n) = 9*A138148(n) + 2*10^n = A002283(2n+1) - 7*10^n.
%F A332192 G.f.: (2 + 707*x - 1600*x^2)/((1 - x)*(1 - 10*x)*(1 - 100*x)).
%F A332192 a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n > 2.
%p A332192 A332192 := n -> 10^(n*2+1)-1-7*10^n;
%t A332192 Array[ 10^(2 # +1) -1 -7*10^# &, 15, 0]
%t A332192 LinearRecurrence[{111,-1110,1000},{2,929,99299},20] (* _Harvey P. Dale_, Nov 07 2022 *)
%o A332192 (PARI) apply( {A332192(n)=10^(n*2+1)-1-7*10^n}, [0..15])
%o A332192 (Python) def A332192(n): return 10**(n*2+1)-1-7*10^n
%Y A332192 Cf. (A077778-1)/2 = A115073: indices of primes.
%Y A332192 Cf. A002275 (repunits R_n = (10^n-1)/9), A002283 (9*R_n), A011557 (10^n).
%Y A332192 Cf. A138148 (cyclops numbers with binary digits only), A002113 (palindromes).
%Y A332192 Cf. A332190 .. A332197, A181965 (variants with different middle digit 0, ..., 8).
%Y A332192 Cf. A332112 .. A332182 (variants with different repeated digit 1, ..., 8).
%K A332192 nonn,base,easy
%O A332192 0,1
%A A332192 _M. F. Hasler_, Feb 08 2020