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A125725 Numbers whose base-7 representation is 222....2. 2
0, 2, 16, 114, 800, 5602, 39216, 274514, 1921600, 13451202, 94158416, 659108914, 4613762400, 32296336802, 226074357616, 1582520503314, 11077643523200, 77543504662402, 542804532636816, 3799631728457714, 26597422099204000 (list; graph; refs; listen; history; text; internal format)
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: A288971 A288970 A037564 * 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

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Last modified May 9 07:33 EDT 2021. Contains 343692 sequences. (Running on oeis4.)