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A037577 Base 5 digits are, in order, the first n terms of the periodic sequence with initial period 1,3. 2
1, 8, 41, 208, 1041, 5208, 26041, 130208, 651041, 3255208, 16276041, 81380208, 406901041, 2034505208, 10172526041, 50862630208, 254313151041, 1271565755208, 6357828776041, 31789143880208, 158945719401041, 794728597005208 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (5,1,-5).

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

EXAMPLE

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

MATHEMATICA

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

CROSSREFS

Sequence in context: A188180 A026968 A026978 * A265149 A209822 A051737

Adjacent sequences:  A037574 A037575 A037576 * A037578 A037579 A037580

KEYWORD

nonn,base,easy

AUTHOR

Clark Kimberling

EXTENSIONS

First formula corrected by Philippe Deléham, Nov 14 2013

STATUS

approved

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Last modified September 24 04:42 EDT 2020. Contains 337317 sequences. (Running on oeis4.)