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) - (2*k+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).
E.g.f.: exp(x)*(exp(6*x) + x). - Elmo R. Oliveira, Mar 05 2025
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]
LinearRecurrence[{9, -15, 7}, {1, 8, 51}, 30] (* Harvey P. Dale, Jun 16 2025 *)
PROG
(Magma) [7^n+n: n in [0..20]];
(Magma) 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
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Jun 16 2013
STATUS
approved