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A024128
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a(n) = 11^n - n.
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9
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1, 10, 119, 1328, 14637, 161046, 1771555, 19487164, 214358873, 2357947682, 25937424591, 285311670600, 3138428376709, 34522712143918, 379749833583227, 4177248169415636, 45949729863572145, 505447028499293754
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OFFSET
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0,2
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COMMENTS
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Smallest prime of this form is a(18) = 5559917313492231463. - Bruno Berselli, Jun 17 2013
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..300
Index entries for linear recurrences with constant coefficients, signature (13,-23,11).
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FORMULA
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G.f.: (1-3*x+12*x^2)/((1-11*x) (1-x)^2). - Vincenzo Librandi, Jun 17 2013
a(n) = 13*a(n-1) - 23*a(n-2) + 11*a(n-3). - Vincenzo Librandi, Jun 17 2013
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MATHEMATICA
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Table[11^n - n, {n, 0, 20}] (* or *) CoefficientList[Series[(1 - 3 x + 12 x^2) / ((1 - 11 x) (1 - x)^2), {x, 0, 30}], x] (* Vincenzo Librandi, Jun 17 2013 *)
LinearRecurrence[{13, -23, 11}, {1, 10, 119}, 20] (* Harvey P. Dale, Aug 02 2017 *)
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PROG
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(MAGMA) [11^n-n: n in [0..20]]; // Vincenzo Librandi, Jul 01 2011
(PARI) a(n)=11^n-n \\ Charles R Greathouse IV, Jul 01 2011
(MAGMA) I:=[1, 10, 119]; [n le 3 select I[n] else 13*Self(n-1)-23*Self(n-2)+11*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Jun 17 2013
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CROSSREFS
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Cf. numbers of the form k^n-n: A000325 (k=2), A024024 (k=3), A024037 (k=4), A024050 (k=5), A024063 (k=6), A024076 (k=7), A024089 (k=8), A024102 (k=9), A024115 (k=10), this sequence (k=11), A024141 (k=12).
Cf. A199030 (first differences).
Sequence in context: A160601 A338975 A327653 * A289215 A223010 A030022
Adjacent sequences: A024125 A024126 A024127 * A024129 A024130 A024131
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane
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STATUS
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approved
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