A226201 a(n) = 8^n + n.

1, 9, 66, 515, 4100, 32773, 262150, 2097159, 16777224, 134217737, 1073741834, 8589934603, 68719476748, 549755813901, 4398046511118, 35184372088847, 281474976710672, 2251799813685265, 18014398509482002, 144115188075855891, 1152921504606846996

Offset

0,2

Comments

Smallest prime of this form is a(101). - 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 (10,-17,8).

Formula

G.f.: (-1+x+7*x^2)/((8*x-1)*(x-1)^2).

a(n) = 10*a(n-1)-17*a(n-2)+8*a(n-3).

Mathematica

Table[8^n + n, {n, 0, 30}] (* or *) CoefficientList[Series[(-1 + x + 7 x^2) / ((8 x - 1) (x - 1)^2), {x, 0, 30}], x]
LinearRecurrence[{10, -17, 8}, {1, 9, 66}, 30] (* Harvey P. Dale, Aug 11 2015 *)

Prog

(Magma) [8^n+n: n in [0..30]]; /* or */ I:=[1, 9, 66]; [n le 3 select I[n] else 10*Self(n-1)-17*Self(n-2)+8*Self(n-3): n in [1..30]];
(PARI) a(n)=8^n+n \\ Charles R Greathouse IV, Oct 07 2015

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), this sequence (k=8), A226202 (k=9), A081552 (k=10), A226737 (k=11).

Cf. A199555 (first differences).

Sequence in context: A048439 A134432 A098107 * A091647 A321945 A232018

Adjacent sequences: A226198 A226199 A226200 * A226202 A226203 A226204

Keyword

nonn,easy

Author

Vincenzo Librandi, Jun 16 2013

Status

approved