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, 2384185791015647, 11920928955078148, 59604644775390649

Offset: 0

Author

Zak Seidov, Mar 23 2005

Keywords

• nonn
• easy

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).

Crossrefs

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

Programs

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

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 *)

PARI

a(n)=5^n+n \\ Charles R Greathouse IV, Oct 07 2015

Formula

From Vincenzo Librandi, Jun 16 2013: (Start)

G.f.: (1-x-4*x^2)/((1-5*x)*(1-x)^2).

a(n) = 7*a(n-1) - 11*a(n-2) + 5*a(n-3). (End)

E.g.f.: exp(x)*(exp(4*x) + x). - Elmo R. Oliveira, Mar 05 2025

Extensions

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