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A086578
a(n) = 7*(10^n - 1).
9
0, 63, 693, 6993, 69993, 699993, 6999993, 69999993, 699999993, 6999999993, 69999999993, 699999999993, 6999999999993, 69999999999993, 699999999999993, 6999999999999993, 69999999999999993, 699999999999999993, 6999999999999999993, 69999999999999999993, 699999999999999999993
OFFSET
0,2
COMMENTS
Original definition: a(n) = k where R(k+7) = 7.
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
MATHEMATICA
LinearRecurrence[{11, -10}, {0, 63}, 31] (* G. C. Greubel, Apr 14 2023 *)
PROG
(Magma) [7*(10^n -1): n in [0..20]]; // G. C. Greubel, Apr 14 2023
(SageMath) [7*(10^n -1) for n in range(21)] # G. C. Greubel, Apr 14 2023
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).
Sequence in context: A152731 A090028 A152725 * A198399 A221968 A115152
KEYWORD
nonn
AUTHOR
Ray Chandler, Jul 22 2003
EXTENSIONS
Edited by Jinyuan Wang, Aug 04 2021
STATUS
approved