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A168415
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a(n) = 2^n + 7.
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11
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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
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OFFSET
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0,1
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COMMENTS
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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
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-2).
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FORMULA
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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
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MATHEMATICA
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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 *)
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PROG
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(PARI) a(n)=1<<n+7 \\ Charles R Greathouse IV, Sep 20 2011
(Magma) [2^n+7: n in [0..40]]; // Vincenzo Librandi, Sep 19 2013
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CROSSREFS
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Cf. A000079, A057195, A104066, A125247, A257272.
Sequence in context: A120176 A139049 A048590 * A199635 A131864 A347392
Adjacent sequences: A168412 A168413 A168414 * A168416 A168417 A168418
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KEYWORD
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nonn,easy
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AUTHOR
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Vincenzo Librandi, Dec 01 2009
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STATUS
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approved
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