%I #13 Feb 11 2020 08:26:41

%S 5,757,77577,7775777,777757777,77777577777,7777775777777,

%T 777777757777777,77777777577777777,7777777775777777777,

%U 777777777757777777777,77777777777577777777777,7777777777775777777777777,777777777777757777777777777,77777777777777577777777777777,7777777777777775777777777777777

%N a(n) = 7*(10^(2n+1)-1)/9 - 2*10^n.

%C See A183180 = {0, 1, 7, 13, 58, 129, 253, ...} for the indices of primes.

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/7/77577.htm">Factorization of 77...77577...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) + 5*10^n.

%F G.f.: (5 + 202*x - 900*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) - 18*exp(9*x) - 7). - _Stefano Spezia_, Feb 08 2020

%p A332175 := n -> 7*(10^(n*2+1)-1)/9 - 2*10^n;

%t Array[7 (10^(2 # + 1) - 1)/9 - 2*10^# &, 15, 0]

%o (PARI) apply( {A332175(n)=10^(n*2+1)\9*7-2*10^n}, [0..15])

%o (Python) def A332175(n): return 10**(n*2+1)//9*7-2*10^n

%Y Cf. (A077785-1)/2 = A183180: indices of primes.

%Y Cf. A138148 (cyclops numbers with binary digits only).

%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