A086578 a(n) = 7*(10^n - 1).

0, 63, 693, 6993, 69993, 699993, 6999993, 69999993, 699999993, 6999999993, 69999999993, 699999999993, 6999999999993, 69999999999993, 699999999999993, 6999999999999993, 69999999999999993, 699999999999999993, 6999999999999999993, 69999999999999999993, 699999999999999999993

Offset: 0

Author

Ray Chandler, Jul 22 2003

Keywords

• nonn
• easy

Comments

Original definition: a(n) = k where R(k+7) = 7.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..500
• Index entries for linear recurrences with constant coefficients, signature (11,-10).

Crossrefs

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

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.

Sequences of the form m*10^n - 7: 3*A033175 (m=1, 10), A086943 (m=3), 3*A185127 (m=4), this sequence (m=7), A100412 (m=8).

Programs

Magma

[7*(10^n -1): n in [0..20]]; // G. C. Greubel, Apr 14 2023

Mathematica

LinearRecurrence[{11,-10}, {0,63}, 31] (* G. C. Greubel, Apr 14 2023 *)

SageMath

[7*(10^n -1) for n in range(21)] # G. C. Greubel, Apr 14 2023

Formula

a(n) = 7*9*A002275(n) = 7*A002283(n).

R(a(n)) = A086575(n).

From Chai Wah Wu, Jul 08 2016: (Start)

a(n) = 11*a(n-1) - 10*a(n-2) for n > 1.

G.f.: 63*x/((1 - x)*(1 - 10*x)). (End)

E.g.f.: 7*(exp(10*x) - exp(x)). - G. C. Greubel, Apr 14 2023

Extensions

Edited by Jinyuan Wang, Aug 04 2021