A125725 Numbers whose base-7 representation is 222....2.

0, 2, 16, 114, 800, 5602, 39216, 274514, 1921600, 13451202, 94158416, 659108914, 4613762400, 32296336802, 226074357616, 1582520503314, 11077643523200, 77543504662402, 542804532636816, 3799631728457714, 26597422099204000

Offset: 1

Author

Zerinvary Lajos, Feb 02 2007

Keywords

• easy
• nonn
• base

Examples

			base 7.......decimal
0..................0
2..................2
22................16
222..............114
2222.............800
22222...........5602
222222.........39216
2222222.......274514
22222222.....1921600
222222222...13451202
etc...........etc.
		

Links

• Davis Smith, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (8,-7).

Crossrefs

Cf. A007310, A023000, A047522, A165759.

Cf. also A002276, A005610, A020988, A024023, A125831, A125835, A125857 for related or similarly constructed sequences.

Programs

GAP

List([1..25], n-> (7^(n-1) -1)/3); # G. C. Greubel, May 23 2019

Magma

[0] cat [n:n in [1..15000000]| Set(Intseq(n,7)) subset [2]]; // Marius A. Burtea, May 06 2019

Magma

[(7^(n-1)-1)/3: n in [1..25]]; // Marius A. Burtea, May 06 2019

Maple

seq(2*(7^n-1)/6, n=0..25);

Mathematica

FromDigits[#,7]&/@Table[PadLeft[{2},n,2],{n,0,25}]  (* Harvey P. Dale, Apr 13 2011 *)
(7^(Range[25]-1) - 1)/3 (* G. C. Greubel, May 23 2019 *)

PARI

vector(25, n, (7^(n-1)-1)/3) \\ Davis Smith, Apr 04 2019

Sage

[(7^(n-1) -1)/3 for n in (1..25)] # G. C. Greubel, May 23 2019

Formula

a(n) = (7^(n-1) - 1)/3 = 2*A023000(n-1).

a(n) = 7*a(n-1) + 2, with a(1)=0. - Vincenzo Librandi, Sep 30 2010

G.f.: 2*x^2 / ( (1-x)*(1-7*x) ). - R. J. Mathar, Sep 30 2013

From Davis Smith, Apr 04 2019: (Start)

A007310(a(n) + 1) = 7^(n - 1).

A047522(a(n + 1)) = -1*A165759(n). (End)

E.g.f.: (exp(7*x) - 7*exp(x) + 6)/21. - Stefano Spezia, Jan 12 2025

Extensions

Offset corrected by N. J. A. Sloane, Oct 02 2010