A226202 a(n) = 9^n + n.

1, 10, 83, 732, 6565, 59054, 531447, 4782976, 43046729, 387420498, 3486784411, 31381059620, 282429536493, 2541865828342, 22876792454975, 205891132094664, 1853020188851857, 16677181699666586, 150094635296999139, 1350851717672992108, 12157665459056928821, 109418989131512359230

Offset: 0

Author

Vincenzo Librandi, Jun 16 2013

Keywords

• nonn
• easy

Comments

After 83, the next prime of this form is a(76). - Bruno Berselli, Jun 18 2013

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..300
• Index entries for linear recurrences with constant coefficients, signature (11,-19,9).

Crossrefs

Cf. numbers of the form k^n + n: A006127 (k=2), A104743 (k=3), A158879 (k=4), A104745 (k=5), A226200 (k=6), A226199 (k=7), A226201 (k=8), this sequence (k=9), A081552 (k=10), A226737 (k=11).

Cf. A199677 (first differences).

Programs

Magma

[9^n+n: n in [0..30]];

Magma

I:=[1, 10, 83]; [n le 3 select I[n] else 11*Self(n-1)-19*Self(n-2)+9*Self(n-3): n in [1..30]];

Mathematica

Table[9^n + n, {n, 0, 30}] (* or *) CoefficientList[Series[(- 1 + x + 8 x^2) / ((9 x - 1) (x - 1)^2), {x, 0, 30}], x]
LinearRecurrence[{11,-19,9},{1,10,83},20] (* Harvey P. Dale, Feb 03 2016 *)

PARI

a(n)=9^n+n \\ Charles R Greathouse IV, Oct 07 2015

Formula

G.f.: (-1+x+8*x^2)/((9*x-1)*(x-1)^2).

a(n) = 11*a(n-1) - 19*a(n-2) + 9*a(n-3).

E.g.f.: exp(x)*(exp(8*x) + x). - Elmo R. Oliveira, Sep 09 2024