This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A086578 #22 Feb 21 2025 23:50:17
%S A086578 0,63,693,6993,69993,699993,6999993,69999993,699999993,6999999993,
%T A086578 69999999993,699999999993,6999999999993,69999999999993,
%U A086578 699999999999993,6999999999999993,69999999999999993,699999999999999993,6999999999999999993,69999999999999999993,699999999999999999993
%N A086578 a(n) = 7*(10^n - 1).
%C A086578 Original definition: a(n) = k where R(k+7) = 7.
%H A086578 G. C. Greubel, <a href="/A086578/b086578.txt">Table of n, a(n) for n = 0..500</a>
%H A086578 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (11,-10).
%F A086578 a(n) = 7*9*A002275(n) = 7*A002283(n).
%F A086578 R(a(n)) = A086575(n).
%F A086578 From _Chai Wah Wu_, Jul 08 2016: (Start)
%F A086578 a(n) = 11*a(n-1) - 10*a(n-2) for n > 1.
%F A086578 G.f.: 63*x/((1 - x)*(1 - 10*x)). (End)
%F A086578 E.g.f.: 7*(exp(10*x) - exp(x)). - _G. C. Greubel_, Apr 14 2023
%t A086578 LinearRecurrence[{11,-10}, {0,63}, 31] (* _G. C. Greubel_, Apr 14 2023 *)
%o A086578 (Magma) [7*(10^n -1): n in [0..20]]; // _G. C. Greubel_, Apr 14 2023
%o A086578 (SageMath) [7*(10^n -1) for n in range(21)] # _G. C. Greubel_, Apr 14 2023
%Y A086578 Cf. A002275, A004086 (R(n)).
%Y A086578 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.
%Y A086578 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).
%K A086578 nonn,easy
%O A086578 0,2
%A A086578 _Ray Chandler_, Jul 22 2003
%E A086578 Edited by _Jinyuan Wang_, Aug 04 2021