A086574 a(n) = 3*(10^n - 1).

0, 27, 297, 2997, 29997, 299997, 2999997, 29999997, 299999997, 2999999997, 29999999997, 299999999997, 2999999999997, 29999999999997, 299999999999997, 2999999999999997, 29999999999999997, 299999999999999997, 2999999999999999997, 29999999999999999997, 299999999999999999997

Offset: 0

Author

Ray Chandler, Jul 22 2003

Keywords

• nonn
• easy

Comments

Original definition: a(n) = k where R(k+3) = 3. [Here R = reverse = A004086, not R = repunit = A002275 as in some other places.]

The restriction to positive indices yields A083813. - M. F. Hasler, Jul 29 2016

Links

• Index entries for linear recurrences with constant coefficients, signature (11,-10).

Crossrefs

Cf. A002275, A004086 (R(n)), A083813.

Cf. One of family of sequences of form a(n) = k, where R(k+m) = m, m=1 to 9; m=1: A002283, m=2: A086573, m=3: A086574, m=4: A086575, m=5: A086576, m=6: A086577, m=7: A086578, m=8: A086579, m=9: A086580.

Programs

Mathematica

Join[{0},Table[FromDigits[Join[PadRight[{2},n,9],{7}]],{n,20}]] (* or *) LinearRecurrence[{11,-10},{0,27},30] (* Harvey P. Dale, Nov 28 2015 *)

PARI

a(n)=10^n*3-3 \\ M. F. Hasler, Jul 29 2016

Formula

a(n) = 3*9*A002275(n) = 3*A002283(n).

R(a(n)) = A086579(n).

a(n) = 11*a(n-1) - 10*a(n-2) with a(0)=0 and a(1)=27. - Harvey P. Dale, Nov 28 2015

G.f.: 27*x/((1 - x)*(1 - 10*x)). - Ilya Gutkovskiy, Jul 29 2016

E.g.f.: 3*exp(x)*(exp(9*x) - 1). - Elmo R. Oliveira, Sep 12 2024

Extensions

Edited by M. F. Hasler, Jul 29 2016