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 A127316 #38 Nov 09 2024 02:23:04
%S A127316 71,73,79,89,103,121,143,169,199,233,271,313,359,409,463,521,583,649,
%T A127316 719,793,871,953,1039,1129,1223,1321,1423,1529,1639,1753,1871,1993,
%U A127316 2119,2249,2383,2521,2663,2809,2959,3113,3271,3433,3599,3769,3943,4121,4303,4489
%N A127316 a(n) = 2*n^2 - 4*n + 73.
%C A127316 Extrapolates a quadratic passing through 71, 73, and 79.
%H A127316 Michael M. Ross, <a href="http://naturalnumbers.org/polyprimes.html">Poly Primes: The Polynomiality of Proximate Primes</a>.
%H A127316 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A127316 G.f.: x*(71 - 140*x + 73*x^2)/(1 - x)^3. - _Arkadiusz Wesolowski_, Oct 24 2013
%F A127316 Sum_{n>=1} 1/a(n) = 1/142 + coth(sqrt(71/2)*Pi)/(2*sqrt(142)). - _Amiram Eldar_, Jul 30 2024
%F A127316 From _Elmo R. Oliveira_, Nov 03 2024: (Start)
%F A127316 E.g.f.: exp(x)*(2*x^2 - 2*x + 73) - 73.
%F A127316 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 3. (End)
%e A127316 If n=10 then 2*n^2 - 4*n + 73 = 233.
%t A127316 Table[2*n^2 - 4*n + 73, {n, 48}] (* _Arkadiusz Wesolowski_, Oct 24 2013 *)
%o A127316 (Magma) [2*n^2-4*n+73 : n in [1..48]]; // _Arkadiusz Wesolowski_, Oct 24 2013
%o A127316 (PARI) vector(48, n, 2*n^2-4*n+73) \\ _Arkadiusz Wesolowski_, Oct 24 2013
%Y A127316 Cf. A126665, A126719.
%K A127316 easy,nonn
%O A127316 1,1
%A A127316 _Michael M. Ross_, Mar 28 2007
%E A127316 Extended by _Charles R Greathouse IV_, Jul 25 2010