A125833 Numbers whose base-5 representation is 333333.......3.

0, 3, 18, 93, 468, 2343, 11718, 58593, 292968, 1464843, 7324218, 36621093, 183105468, 915527343, 4577636718, 22888183593, 114440917968, 572204589843, 2861022949218, 14305114746093, 71525573730468, 357627868652343

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (6,-5).

Formula

a(n) = 3*(5^n - 1)/4.

a(n) = 5*a(n-1) + 3 for n > 0, a(0)=0. - Vincenzo Librandi, Sep 30 2010

From G. C. Greubel, Aug 03 2019: (Start)

a(n) = 3*A003463(n).

G.f.: 3*x/((1-x)*(1-5*x)).

E.g.f.: 3*(exp(5*x) - exp(x))/4. (End)

Example

Base 5.................decimal
0.........................0
3.........................3
33.......................18
333......................93
3333....................468
33333..................2343
333333................11718
3333333...............58593
33333333.............292968, etc.

Maple

seq(3*(5^n-1)/4, n=0..30);

Mathematica

Table[FromDigits[PadRight[{}, n, 3], 5], {n, 0, 30}] (* or *) LinearRecurrence[ {6, -5}, {0, 3}, 30] (* Harvey P. Dale, Sep 23 2016 *)
3*(5^Range[0, 30] -1)/4 (* G. C. Greubel, Aug 03 2019 *)

Prog

(PARI) vector(30, n, n--; 3*(5^n -1)/4) \\ G. C. Greubel, Aug 03 2019
(Magma) [3*(5^n -1)/4: n in [0..30]]; // G. C. Greubel, Aug 03 2019
(Sage) [3*(5^n -1)/4 for n in (0..30)] # G. C. Greubel, Aug 03 2019
(GAP) List([0..30], n-> 3*(5^n -1)/4); G. C. Greubel, Aug 03 2019

Crossrefs

Cf. A003463.

Sequence in context: A064671 A363647 A058409 * A129547 A081151 A132848

Adjacent sequences: A125830 A125831 A125832 * A125834 A125835 A125836

Keyword

nonn,easy

Author

Zerinvary Lajos, Feb 03 2007

Status

approved