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

1,2

Links

Davis Smith, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (8,-7).

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)

Example

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.

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 *)

Prog

(PARI) vector(25, n, (7^(n-1)-1)/3) \\ Davis Smith, Apr 04 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
(Sage) [(7^(n-1) -1)/3 for n in (1..25)] # G. C. Greubel, May 23 2019
(GAP) List([1..25], n-> (7^(n-1) -1)/3) # G. C. Greubel, May 23 2019

Crossrefs

Cf. A007310, A023000, A047522, A165759.

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

Sequence in context: A288970 A037564 A361743 * A288965 A207420 A207736

Adjacent sequences: A125722 A125723 A125724 * A125726 A125727 A125728

Keyword

easy,nonn,base

Author

Zerinvary Lajos, Feb 02 2007

Extensions

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

Status

approved