This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A332171 #32 Apr 04 2024 15:06:17
%S A332171 1,717,77177,7771777,777717777,77777177777,7777771777777,
%T A332171 777777717777777,77777777177777777,7777777771777777777,
%U A332171 777777777717777777777,77777777777177777777777,7777777777771777777777777,777777777777717777777777777,77777777777777177777777777777,7777777777777771777777777777777
%N A332171 a(n) = 7*(10^(2n+1)-1)/9 - 6*10^n.
%C A332171 For n == 0 or n == 2 (mod 6), there is no obvious divisibility pattern.
%C A332171 According to M. Kamada, n = 116 is the only index of a prime up to n = 10^5.
%H A332171 Makoto Kamada, <a href="https://stdkmd.net/nrr/7/77177.htm">Factorization of 77...77177...77</a>.
%H A332171 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (111,-1110,1000).
%F A332171 a(n) = 7*A138148(n) + 10^n.
%F A332171 For n == 1 (mod 3), 3 | a(n) and a(n)/3 = 259*(10^(2n+1)-1)/999 - 2*10^n;
%F A332171 for n == 3 or 5 (mod 6), 13 | a(n) and a(n)/13 = (A(n)-1)*10^n + B(n), where A(n) (resp. B(n)) are the n leftmost (resp. rightmost) digits of 59829*(10^(ceiling(n/6)*6)-1)/(10^6-1).
%F A332171 From _Colin Barker_, Feb 07 2020: (Start)
%F A332171 G.f.: (1 + 606*x - 1300*x^2) / ((1 - x)*(1 - 10*x)*(1 - 100*x)).
%F A332171 a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n>2.
%F A332171 (End)
%F A332171 E.g.f.: (1/9)*exp(x)*(70*exp(99*x) - 54*exp(9*x) - 7). - _Stefano Spezia_, Feb 08 2020
%t A332171 Array[7 (10^(2 # + 1) - 1)/9 - 6*10^# &, 15, 0] (* or *)
%t A332171 CoefficientList[Series[(1 + 606 x - 1300 x^2)/((1 - x) (1 - 10 x) (1 - 100 x)), {x, 0, 15}], x] (* _Michael De Vlieger_, Feb 08 2020 *)
%t A332171 Table[FromDigits[Join[PadRight[{},n,7],{1},PadRight[{},n,7]]],{n,0,20}] (* or *) LinearRecurrence[ {111,-1110,1000},{1,717,77177},20] (* _Harvey P. Dale_, Apr 04 2024 *)
%o A332171 (PARI) apply( {A332171(n)=10^(n*2+1)\9*7-6*10^n}, [0..15])
%o A332171 (PARI) Vec((1 + 606*x - 1300*x^2) / ((1 - x)*(1 - 10*x)*(1 - 100*x)) + O(x^15)) \\ _Colin Barker_, Feb 07 2020
%o A332171 (Python) def A332171(n): return 10**(n*2+1)//9*7-6*10^n
%Y A332171 Cf. A138148 (cyclops numbers with binary digits only), A002113 (palindromes).
%Y A332171 Cf. A002275 (repunits R_n = [10^n/9]), A002281 (7*R_n), A011557 (10^n).
%Y A332171 Cf. A332121 .. A332191 (variants with different repeated digit 2, ..., 9).
%Y A332171 Cf. A332170 .. A332179 (variants with different middle digit 2, ..., 9).
%K A332171 nonn,base,easy
%O A332171 0,2
%A A332171 _M. F. Hasler_, Feb 06 2020