A024128 a(n) = 11^n - n.

1, 10, 119, 1328, 14637, 161046, 1771555, 19487164, 214358873, 2357947682, 25937424591, 285311670600, 3138428376709, 34522712143918, 379749833583227, 4177248169415636, 45949729863572145, 505447028499293754, 5559917313492231463, 61159090448414546272, 672749994932560009181

Offset

0,2

Comments

Smallest prime of this form is a(18) = 5559917313492231463. - Bruno Berselli, Jun 17 2013

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..300

Index entries for linear recurrences with constant coefficients, signature (13,-23,11).

Formula

From Vincenzo Librandi, Jun 17 2013: (Start)

G.f.: (1-3*x+12*x^2)/((1-11*x) (1-x)^2).

a(n) = 13*a(n-1) - 23*a(n-2) + 11*a(n-3). (End)

E.g.f.: exp(x)*(exp(10*x) - x). - Elmo R. Oliveira, Sep 10 2024

Mathematica

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 *)

Prog

(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

Crossrefs

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

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved