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Numbers whose base 7 representation is 555....5.
0

%I #16 Dec 22 2024 09:30:55

%S 0,5,40,285,2000,14005,98040,686285,4804000,33628005,235396040,

%T 1647772285,11534406000,80740842005,565185894040,3956301258285,

%U 27694108808000,193858761656005,1357011331592040,9499079321144285

%N Numbers whose base 7 representation is 555....5.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8,-7).

%F a(n) = 5*(7^(n-1)-1)/6 = 5*A023000(n-1).

%F a(n) = 7*a(n-1) + 5 for n > 1. - _Vincenzo Librandi_, Sep 30 2010

%F G.f.: 5*x^2 / ( (7*x-1)*(x-1) ). - _R. J. Mathar_, Sep 30 2013

%e Base 7.............decimal

%e 0........................0

%e 5........................5

%e 55......................40

%e 555....................285

%e 5555..................2000

%e 55555................14005

%e 555555...............98040

%e 5555555.............686285

%e 55555555...........4804000

%e 555555555.........33628005

%e etc....................etc...

%p seq(5*(7^n-1)/6, n=0..21);

%t Table[FromDigits[Table[5,n],7],{n,0,19}] (* _James C. McMahon_, Dec 21 2024 *)

%K easy,nonn

%O 1,2

%A _Zerinvary Lajos_, Feb 02 2007