A168415 a(n) = 2^n + 7.

8, 9, 11, 15, 23, 39, 71, 135, 263, 519, 1031, 2055, 4103, 8199, 16391, 32775, 65543, 131079, 262151, 524295, 1048583, 2097159, 4194311, 8388615, 16777223, 33554439, 67108871, 134217735, 268435463, 536870919, 1073741831, 2147483655

Offset: 0

Author

Vincenzo Librandi, Dec 01 2009

Keywords

• nonn
• easy

Comments

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

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-2).

Crossrefs

Cf. A000079, A057195, A104066, A125247, A257272.

Programs

Magma

[2^n+7: n in [0..40]]; // Vincenzo Librandi, Sep 19 2013

Mathematica

a[n_]:=2^n+7; a[Range[0,200]] (* Vladimir Joseph Stephan Orlovsky, Feb 20 2011*)
CoefficientList[Series[(8 - 15 x)/((2 x - 1) (x - 1)), {x, 0, 200}], x] (* Vincenzo Librandi, Sep 19 2013 *)
LinearRecurrence[{3,-2},{8,9},40] (* Harvey P. Dale, Mar 03 2014 *)

PARI

a(n)=1<Charles R Greathouse IV, Sep 20 2011

Formula

a(n) = 2*a(n-1) - 7, n > 1.

G.f.: (8 - 15*x)/((2*x - 1)*(x - 1)). - R. J. Mathar, Jul 10 2011

a(n) = A000079(n) + 7. - Omar E. Pol, Sep 20 2011

E.g.f.: exp(2*x) + 7*exp(x). - G. C. Greubel, Jul 22 2016

a(n) = 3*a(n-1) - 2*a(n-2) for n > 1. - Elmo R. Oliveira, Nov 11 2023