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%I #12 Feb 11 2020 08:26:38
%S 4,747,77477,7774777,777747777,77777477777,7777774777777,
%T 777777747777777,77777777477777777,7777777774777777777,
%U 777777777747777777777,77777777777477777777777,7777777777774777777777777,777777777777747777777777777,77777777777777477777777777777,7777777777777774777777777777777
%N a(n) = 7*(10^(2n+1)-1)/9 - 3*10^n.
%C See A183179 = {2, 3, 6, 23, 36, 69, 561, ...} for the indices of primes.
%H Makoto Kamada, <a href="https://stdkmd.net/nrr/7/77477.htm">Factorization of 77...77477...77</a>, updated Dec 11 2018.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (111,-1110,1000).
%F a(n) = 7*A138148(n) + 4*10^n.
%F G.f.: (4 + 303*x - 1000*x^2)/((1 - x)*(1 - 10*x)*(1 - 100*x)).
%F a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n>2.
%F E.g.f.: (1/9)*exp(x)*(70*exp(99*x) - 27*exp(9*x) - 7). - _Stefano Spezia_, Feb 08 2020
%p A332174 := n -> 7*(10^(n*2+1)-1)/9 - 3*10^n;
%t Array[7 (10^(2 # + 1) - 1)/9 - 3*10^# &, 15, 0]
%o (PARI) apply( {A332174(n)=10^(n*2+1)\9*7-3*10^n}, [0..15])
%o (Python) def A332174(n): return 10**(n*2+1)//9*7-3*10^n
%Y Cf. A138148 (cyclops numbers with binary digits only).
%Y Cf. (A077781-1)/2 = A183179: indices of primes.
%Y Cf. A002275 (repunits R_n = (10^n-1)/9), A002281 (7*R_n), A011557 (10^n).
%Y Cf. A332171 .. A332179 (variants with different middle digit 1, ..., 9).
%K nonn,base,easy
%O 0,1
%A _M. F. Hasler_, Feb 08 2020
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