A004663 Powers of 3 written in base 9.

1, 3, 10, 30, 100, 300, 1000, 3000, 10000, 30000, 100000, 300000, 1000000, 3000000, 10000000, 30000000, 100000000, 300000000, 1000000000, 3000000000, 10000000000, 30000000000, 100000000000, 300000000000, 1000000000000, 3000000000000, 10000000000000, 30000000000000

Offset

0,2

Links

Robert Israel, Table of n, a(n) for n = 0..1997

Index entries for linear recurrences with constant coefficients, signature (0,10).

Formula

From Paul Barry, Jul 14 2004: (Start)

G.f.: (1 + 3*x)/(1 - 10*x^2);

a(n) = 2*a(n-1) + 3*a(n-2) + 10^floor((n-2)/2);

a(n) = Sum_{k=0..floor(n/2)} binomial(floor(n/2), k)*3^(n-2*k). (End)

a(n) = 3*a(n-1) + ((1 + (-1)^n)/2)*a(n-2) with a(0)=1, a(1)=3. - Taras Goy, Mar 20 2019

E.g.f.: cosh(sqrt(10)*x) + 3*sinh(sqrt(10)*x)/sqrt(10). - Stefano Spezia, Mar 31 2023

Maple

seq(op([10^i, 3*10^i]), i=0..100); # Robert Israel, Jun 25 2018

Mathematica

Table[FromDigits[IntegerDigits[3^n, 9]], {n, 0, 100}] (* G. C. Greubel, Oct 12 2018 *)

Prog

(PARI) a(n)=3^bittest(n, 0)*10^(n\2) \\ M. F. Hasler, Jun 25 2018

Crossrefs

Cf. A026383, A016116.

Cf. A000244, A004656, A004658, A004659, ... : powers of 3 in base 10, 2, 4, 5, ...

Cf. A000079, A004642, ..., A004655: powers of 2 written in base 10, 2, 3, ..., 16.

Sequence in context: A003441 A136841 A136846 * A136853 A361911 A215287

Adjacent sequences: A004660 A004661 A004662 * A004664 A004665 A004666

Keyword

nonn,base,easy

Author

N. J. A. Sloane

Status

approved