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%I #69 Nov 07 2020 22:16:02
%S 1,7,11,71,111,711,1111,7111,11111,71111,111111,711111,1111111,
%T 7111111,11111111,71111111,111111111,711111111,1111111111,7111111111,
%U 11111111111,71111111111,111111111111,711111111111,1111111111111,7111111111111,11111111111111,71111111111111
%N Largest positive number using exactly n segments on a calculator display (when '6' and '7' are represented using 6 resp. 3 segments).
%C The sequence begins with a(2) = 1 since at least two segments are needed to form any digit. It requires two segments to form the digit 1 and three segments to form the digit 7.
%C All other digits use more than 3 segments.
%H <a href="/index/Ca#calculatordisplay">Index entries for sequences related to calculator display</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,10,-10).
%F a(n+2) = 10*a(n) + 1 for n >= 2.
%F a(2*n) = (10^n - 1)/9 ; a(2*n + 1) = ((10^n - 1)/9) + 6*10^(n - 1).
%F From _Stefano Spezia_, Sep 29 2020: (Start)
%F G.f.: x^2*(1 + 6*x - 6*x^2)/(1 - x - 10*x^2 + 10*x^3).
%F a(n) = a(n-1) + 10*a(n-2) - 10*a(n-3) for n > 4. (End)
%t CoefficientList[Series[(1 + 6*x - 6*x^2)/(1 - x - 10*x^2 + 10*x^3), {x, 0, 30}], x] (* _Wesley Ivan Hurt_, Nov 07 2020 *)
%Y Cf. A063720 (number of segments), A216261 (smallest number), A249572.
%K nonn,base
%O 2,2
%A _Suren Suren_, Sep 29 2020
%E More terms from _Stefano Spezia_, Sep 29 2020
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