A125835 Numbers whose base-8 or octal representation is 22222222.......2.

0, 2, 18, 146, 1170, 9362, 74898, 599186, 4793490, 38347922, 306783378, 2454267026, 19634136210, 157073089682, 1256584717458, 10052677739666, 80421421917330, 643371375338642, 5146971002709138, 41175768021673106, 329406144173384850, 2635249153387078802, 21081993227096630418

Offset: 1

Author

Zerinvary Lajos, Feb 03 2007

Keywords

• easy
• nonn

Examples

			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.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (9,-8).

Crossrefs

Cf. A023001.

Programs

GAP

List([1..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

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 *)

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

Sage

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

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)

Extensions

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

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