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A332117 a(n) = (10^(2n+1)-1)/9 + 6*10^n.

%I A332117 #7 Feb 11 2020 07:58:20
%S A332117 7,171,11711,1117111,111171111,11111711111,1111117111111,
%T A332117 111111171111111,11111111711111111,1111111117111111111,
%U A332117 111111111171111111111,11111111111711111111111,1111111111117111111111111,111111111111171111111111111,11111111111111711111111111111,1111111111111117111111111111111
%N A332117 a(n) = (10^(2n+1)-1)/9 + 6*10^n.
%C A332117 See A107127 = {0, 3, 33, 311, 2933, ...} for the indices of primes.
%H A332117 Brady Haran and Simon Pampena, <a href="https://youtu.be/HPfAnX5blO0">Glitch Primes and Cyclops Numbers</a>, Numberphile video (2015).
%H A332117 Patrick De Geest, <a href="http://www.worldofnumbers.com/wing.htm#pwp171">Palindromic Wing Primes: (1)7(1)</a>, updated: June 25, 2017.
%H A332117 Makoto Kamada, <a href="https://stdkmd.net/nrr/1/11711.htm">Factorization of 11...11711...11</a>, updated Dec 11 2018.
%H A332117 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (111,-1110,1000).
%F A332117 a(n) = A138148(n) + 7*10^n = A002275(2n+1) + 6*10^n.
%F A332117 G.f.: (7 - 606*x + 500*x^2)/((1 - x)(1 - 10*x)(1 - 100*x)).
%F A332117 a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n > 2.
%p A332117 A332117 := n -> (10^(2*n+1)-1)/9+6*10^n;
%t A332117 Array[(10^(2 # + 1)-1)/9 + 6*10^# &, 15, 0]
%o A332117 (PARI) apply( {A332117(n)=10^(n*2+1)\9+6*10^n}, [0..15])
%o A332117 (Python) def A332117(n): return 10**(n*2+1)//9+6*10**n
%Y A332117 Cf. (A077789-1)/2 = A107127: indices of primes.
%Y A332117 Cf. A002275 (repunits R_n = (10^n-1)/9), A011557 (10^n).
%Y A332117 Cf. A138148 (cyclops numbers with binary digits), A002113 (palindromes).
%Y A332117 Cf. A332127 .. A332197 (variants with different repeated digit 2, ..., 9).
%Y A332117 Cf. A332112 .. A332119 (variants with different middle digit 2, ..., 9).
%K A332117 nonn,base,easy
%O A332117 0,1
%A A332117 _M. F. Hasler_, Feb 09 2020