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

Author

Zerinvary Lajos, Feb 03 2007

Keywords

• nonn
• easy

Examples

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

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (6,-5).

Crossrefs

Cf. A003463.

Programs

GAP

List([0..30], 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

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 *)

PARI

vector(30, n, n--; 3*(5^n -1)/4) \\ G. C. Greubel, Aug 03 2019

Sage

[3*(5^n -1)/4 for n in (0..30)] # G. C. Greubel, Aug 03 2019

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)