|
%I #41 Nov 11 2023 19:56:12
%S 8,9,11,15,23,39,71,135,263,519,1031,2055,4103,8199,16391,32775,65543,
%T 131079,262151,524295,1048583,2097159,4194311,8388615,16777223,
%U 33554439,67108871,134217735,268435463,536870919,1073741831,2147483655
%N a(n) = 2^n + 7.
%C a(n) is prime <=> a(n) is in A104066 <=> n is in A057195 <=> 2^(n-1)*a(n) = A257272(n) is in A125247. - _M. F. Hasler_, Apr 27 2015
%H Vincenzo Librandi, <a href="/A168415/b168415.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).
%F a(n) = 2*a(n-1) - 7, n > 1.
%F G.f.: (8 - 15*x)/((2*x - 1)*(x - 1)). - _R. J. Mathar_, Jul 10 2011
%F a(n) = A000079(n) + 7. - _Omar E. Pol_, Sep 20 2011
%F E.g.f.: exp(2*x) + 7*exp(x). - _G. C. Greubel_, Jul 22 2016
%F a(n) = 3*a(n-1) - 2*a(n-2) for n > 1. - _Elmo R. Oliveira_, Nov 11 2023
%t a[n_]:=2^n+7; a[Range[0,200]] (* _Vladimir Joseph Stephan Orlovsky_, Feb 20 2011*)
%t CoefficientList[Series[(8 - 15 x)/((2 x - 1) (x - 1)), {x, 0, 200}], x] (* _Vincenzo Librandi_, Sep 19 2013 *)
%t LinearRecurrence[{3,-2},{8,9},40] (* _Harvey P. Dale_, Mar 03 2014 *)
%o (PARI) a(n)=1<<n+7 \\ _Charles R Greathouse IV_, Sep 20 2011
%o (Magma) [2^n+7: n in [0..40]]; // _Vincenzo Librandi_, Sep 19 2013
%Y Cf. A000079, A057195, A104066, A125247, A257272.
%K nonn,easy
%O 0,1
%A _Vincenzo Librandi_, Dec 01 2009
|
