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