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A125835 Numbers whose base 8 or octal representation is 22222222.......2. 4
0, 2, 18, 146, 1170, 9362, 74898, 599186, 4793490, 38347922, 306783378, 2454267026, 19634136210, 157073089682, 1256584717458, 10052677739666, 80421421917330, 643371375338642, 5146971002709138, 41175768021673106, 329406144173384850, 2635249153387078802, 21081993227096630418 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (9,-8).

FORMULA

a(n) = 2*(8^(n-1) - 1)/7.

a(n) = 8*a(n-1) + 2, with a(1)=0. - Vincenzo Librandi, Sep 30 2010

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

a(n) = 2*A023001(n).

G.f.: 2*x^2/((1-x)*(1-8*x)).

E.g.f.: 2*(exp(8*x) - exp(x))/7. (End)

EXAMPLE

Octal.............decimal

0.......................0

2.......................2

22.....................18

222...................146

2222.................1170

22222................9362

222222..............74898

2222222............599186

22222222..........4793490

222222222........38347922

2222222222......306783378

etc. ...............etc.

MAPLE

seq(2*(8^n-1)/7, n=0..30);

MATHEMATICA

nxt2[n_]:=Module[{idn=IntegerDigits[n, 8]}, FromDigits[PadLeft[idn, Length[idn]+1, 2], 8]]; Join[{0}, NestList[nxt2, 2, 30]]  (* Harvey P. Dale, Mar 09 2011 *)

Module[{nn=30, c}, c=PadRight[{}, nn, 2]; Table[FromDigits[Take[c, n], 8], {n, 0, nn}]] (* Harvey P. Dale, Sep 05 2015 *)

2*(8^(Range[30]-1) -1)/7 (* G. C. Greubel, Aug 03 2019 *)

PROG

(PARI) a(n)=2*(1<<(3*n-3)\7) \\ Charles R Greathouse IV, Mar 09, 2011

(PARI) vector(30, n, 2*(8^(n-1) -1)/7) \\ G. C. Greubel, Aug 03 2019

(MAGMA) [2*(8^(n-1) -1)/7: n in [1..30]]; // G. C. Greubel, Aug 03 2019

(Sage) [2*(8^(n-1) -1)/7 for n in (1..30)] # G. C. Greubel, Aug 03 2019

(GAP) List([1..30], n-> 2*(8^(n-1) -1)/7); # G. C. Greubel, Aug 03 2019

CROSSREFS

Cf. A023001.

Sequence in context: A290215 A208654 A037565 * A091170 A207319 A091165

Adjacent sequences:  A125832 A125833 A125834 * A125836 A125837 A125838

KEYWORD

easy,nonn

AUTHOR

Zerinvary Lajos, Feb 03 2007

EXTENSIONS

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

Terms a(21) onward added by G. C. Greubel, Aug 03 2019

STATUS

approved

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Last modified October 21 13:57 EDT 2019. Contains 328299 sequences. (Running on oeis4.)