A125836 - OEIS

%I #15 Sep 08 2022 08:45:29

%S 0,5,45,365,2925,23405,187245,1497965,11983725,95869805,766958445,

%T 6135667565,49085340525,392682724205,3141461793645,25131694349165,

%U 201053554793325,1608428438346605,12867427506772845,102939420054182765

%N Numbers whose base 8 or octal representation is 555555555......5.

%H G. C. Greubel, <a href="/A125836/b125836.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (9,-8).

%F a(n) = 5*(8^(n-1) -1)/7 = 5*A023001(n-1).

%F a(n) = 8*a(n-1) + 5, with a(1)=0. - _Vincenzo Librandi_, Sep 30 2010

%F G.f.: 5*x^2/( (1-x)*(1-8*x)). - _R. J. Mathar_, Sep 30 2013

%F From _G. C. Greubel_, Aug 03 2019: (Start)

%F a(n) = 5*A024088(n-1)/7.

%F E.g.f.: 5*(exp(8*x) - exp(x))/7. (End)

%e Octal...............decimal

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

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

%e 55......................45

%e 555....................365

%e 5555..................2925

%e 55555................23405

%e 555555..............187245

%e 5555555............1497965

%e 55555555..........11983725

%e 555555555.........95869805

%e 5555555555.......766958445

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

%p seq(5*(8^n-1)/7, n=0..30);

%t 5*(8^(Range[30]-1) -1)/7 (* _G. C. Greubel_, Aug 03 2019 *)

%o (PARI) vector(30, n, 5*(8^(n-1) -1)/7) \\ _G. C. Greubel_, Aug 03 2019

%o (Magma) [5*(8^(n-1) -1)/7: n in [1..30]]; // _G. C. Greubel_, Aug 03 2019

%o (Sage) [5*(8^(n-1) -1)/7 for n in (1..30)] # _G. C. Greubel_, Aug 03 2019

%o (GAP) List([1..30], n-> 5*(8^(n-1) -1)/7); # _G. C. Greubel_, Aug 03 2019

%Y Cf. A023001, A024088.

%K easy,nonn

%O 1,2

%A _Zerinvary Lajos_, Feb 03 2007