A037577 Base 5 digits are, in order, the first n terms of the periodic sequence with initial period 1,3.

1, 8, 41, 208, 1041, 5208, 26041, 130208, 651041, 3255208, 16276041, 81380208, 406901041, 2034505208, 10172526041, 50862630208, 254313151041, 1271565755208, 6357828776041, 31789143880208, 158945719401041, 794728597005208

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• base
• easy

Comments

This is a particular case of the generalized sequence a(n)=((A^n) - B)/(A-B). Sometimes the primes of this form are of interest, see A001348, A014224, A028491. - Ctibor O. Zizka, Apr 15 2008

Examples

			a(1) = (5-1)/3 = 1, a(2) = (5^2-1)/3 = 8. - _Philippe Deléham_, Nov 15 2013
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (5,1,-5).

Programs

Mathematica

CoefficientList[Series[(3 x + 1)/((x - 1) (x + 1) (5 x - 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 21 2013 *)

Formula

a(n) = (5^n - 2)/3 for n odd ; a(n) = (5^n - 1)/3 for n even. - Ctibor O. Zizka, Apr 15 2008

a(n) = floor(5^n/3). - Gary Detlefs, Sep 06 2010

a(n) = 5*a(n-1) + a(n-2) - 5*a(n-3). - Charles R Greathouse IV, Jan 15 2011

G.f.: x*(3*x+1) / ((x-1)*(x+1)*(5*x-1)). - Colin Barker, Dec 27 2012

Extensions

First formula corrected by Philippe Deléham, Nov 14 2013