A104745 a(n) = 5^n + n.

1, 6, 27, 128, 629, 3130, 15631, 78132, 390633, 1953134, 9765635, 48828136, 244140637, 1220703138, 6103515639, 30517578140, 152587890641, 762939453142, 3814697265643, 19073486328144, 95367431640645, 476837158203146

Offset

0,2

Comments

Numbers m=5^n+n such that equation x=5^(m-x) has solution x=5^n, see A104744.

No primes of the form 5^n+n for n < 7954. - Thomas Ordowski, Oct 28 2013

a(7954) is prime (5560 digits). - Thomas Ordowski, May 07 2015

Links

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

Factordb, 5^7954 + 7954.

Index entries for linear recurrences with constant coefficients, signature (7,-11,5).

Formula

G.f.: (1-x-4*x^2)/((1-5*x)(1-x)^2). - Vincenzo Librandi, Jun 16 2013

a(n) = 7*a(n-1)-11*a(n-2)+5*a(n-3). - Vincenzo Librandi, Jun 16 2013

Maple

g:=1/(1-5*z): gser:=series(g, z=0, 43): seq(coeff(gser, z, n)+n, n=0..31); # Zerinvary Lajos, Jan 09 2009

Mathematica

Table[5^n+n, {n, 0, 40}] (* Vladimir Joseph Stephan Orlovsky, May 19 2011 *)
CoefficientList[Series[(1 - x - 4 x^2) / ((1 - 5 x) (1 - x)^2), {x, 0, 30}], x] (* Vincenzo Librandi, Jun 16 2013 *)
LinearRecurrence[{7, -11, 5}, {1, 6, 27}, 30] (* Harvey P. Dale, Dec 03 2017 *)

Prog

(Magma) I:=[1, 6, 27]; [n le 3 select I[n] else 7*Self(n-1)-11*Self(n-2) +5*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Jun 16 2013
(PARI) a(n)=5^n+n \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

Cf. A104744, A006127, A104743, A158879, A081552, A058046, A181572, A093324.

Sequence in context: A377263 A109115 A038176 * A184279 A299598 A343492

Adjacent sequences: A104742 A104743 A104744 * A104746 A104747 A104748

Keyword

nonn,easy

Author

Zak Seidov, Mar 23 2005

Extensions

More terms from Jonathan R. Love (japanada11(AT)yahoo.ca), Mar 09 2007

Status

approved