A226200 a(n) = 6^n + n.

1, 7, 38, 219, 1300, 7781, 46662, 279943, 1679624, 10077705, 60466186, 362797067, 2176782348, 13060694029, 78364164110, 470184984591, 2821109907472, 16926659444753, 101559956668434, 609359740010515, 3656158440062996, 21936950640377877, 131621703842267158, 789730223053602839

Offset: 0

Author

Vincenzo Librandi, Jun 16 2013

Keywords

• nonn
• easy

Comments

After 7, the next prime of this form has 238 digits (see A058828). - 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 (8,-13,6).

Crossrefs

Cf. numbers of the form k^n + n: A006127 (k=2), A104743 (k=3), A158879 (k=4), A104745 (k=5), this sequence (k=6), A226199 (k=7), A226201 (k=8), A226202 (k=9), A081552 (k=10), A226737 (k=11).

Cf. A058828, A199320 (first differences).

Programs

Magma

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

Magma

I:=[1, 7, 38]; [n le 3 select I[n] else 8*Self(n-1)-13*Self(n-2)+6*Self(n-3): n in [1..30]];

Mathematica

Table[6^n + n, {n, 0, 30}] (* or *) CoefficientList[Series[(-1 + x + 5 x^2) / ((6 x - 1) (x - 1)^2), {x, 0, 30}], x]

PARI

a(n)=6^n+n \\ Charles R Greathouse IV, Oct 07 2015

Formula

G.f.: (-1+x+5*x^2)/((6*x-1)*(x-1)^2).

a(n) = 8*a(n-1) - 13*a(n-2) + 6*a(n-3).

E.g.f.: exp(x)*(exp(5*x) + x). - Elmo R. Oliveira, Mar 05 2025