A107585 a(n) = 5^n - 5*n.

1, 0, 15, 110, 605, 3100, 15595, 78090, 390585, 1953080, 9765575, 48828070, 244140565, 1220703060, 6103515555, 30517578050, 152587890545, 762939453040, 3814697265535, 19073486328030, 95367431640525, 476837158203020, 2384185791015515, 11920928955078010, 59604644775390505, 298023223876953000

Offset: 0

Author

Zak Seidov, May 16 2005

Keywords

• nonn
• easy

Comments

Numbers a(n) = k such that the number m with n 5's and k 1's has digit product = digit sum = 5^n.

Examples

			Corresponding numbers m are 1, 5, 11111111111111155, ...
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (7,-11,5).

Crossrefs

Cf. A107583, A107584.

Programs

Magma

[(5^n - 5*n): n in [0..25]]; // Vincenzo Librandi, Dec 16 2010

Mathematica

Table[5^m-5*m, {m, 0, 10}]
LinearRecurrence[{7,-11,5},{1,0,15},30] (* Harvey P. Dale, Oct 21 2015 *)

PARI

a(n)=5^n-5*n \\ Charles R Greathouse IV, Oct 26 2011

Formula

a(n) = 7*a(n-1) - 11*a(n-2) + 5*a(n-3), n >= 3. - Vincenzo Librandi, Oct 26 2011

G.f.: (-1-26*x^2+7*x)/((5*x-1)*(x-1)^2). - R. J. Mathar, Oct 26 2011

E.g.f.: exp(x)*(exp(4*x) - 5*x). - Elmo R. Oliveira, Sep 10 2024

Extensions

Corrected by Charles R Greathouse IV, Sep 08 2012