A226199 a(n) = 7^n + n.

1, 8, 51, 346, 2405, 16812, 117655, 823550, 5764809, 40353616, 282475259, 1977326754, 13841287213, 96889010420, 678223072863, 4747561509958, 33232930569617, 232630513987224, 1628413597910467, 11398895185373162, 79792266297612021

Offset

0,2

Comments

Smallest prime of this form is a(34) = 54116956037952111668959660883.

In general, the g.f. of a sequence of numbers of the form k^n+n is (1-x-(k-1)*x^2)/((1-k*x)*(x-1)^2) with main linear recurrence (k+2)*a(n-1) -(2k+1)*a(n-2) +k*a(n-3). - Bruno Berselli, Jun 16 2013

Links

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

Index entries for linear recurrences with constant coefficients, signature (9,-15,7).

Formula

G.f.: (1-x-6*x^2)/((1-7*x)*(1-x)^2).

a(n) = 9*a(n-1)-15*a(n-2)+7*a(n-3).

Mathematica

Table[7^n + n, {n, 0, 30}] (* or *) CoefficientList[Series[(1 - x - 6 x^2) / ((1 - 7 x) (1 - x)^2), {x, 0, 20}], x]

Prog

(Magma) [7^n+n: n in [0..20]]; /* or */ I:=[1, 8, 51]; [n le 3 select I[n] else 9*Self(n-1)-15*Self(n-2)+7*Self(n-3): n in [1..30]];
(PARI) a(n)=7^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), this sequence (k=7), A226201 (k=8), A226202 (k=9), A081552 (k=10), A226737 (k=11).

Cf. A199483 (first differences), A370657.

Sequence in context: A048438 A348312 A295602 * A267637 A238648 A341626

Adjacent sequences: A226196 A226197 A226198 * A226200 A226201 A226202

Keyword

nonn,easy

Author

Vincenzo Librandi, Jun 16 2013

Status

approved