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A337099
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Largest positive number using exactly n segments on a calculator display (when '6' and '7' are represented using 6 resp. 3 segments).
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0
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1, 7, 11, 71, 111, 711, 1111, 7111, 11111, 71111, 111111, 711111, 1111111, 7111111, 11111111, 71111111, 111111111, 711111111, 1111111111, 7111111111, 11111111111, 71111111111, 111111111111, 711111111111, 1111111111111, 7111111111111, 11111111111111, 71111111111111
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OFFSET
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2,2
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COMMENTS
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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.
All other digits use more than 3 segments.
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LINKS
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Table of n, a(n) for n=2..29.
Index entries for sequences related to calculator display
Index entries for linear recurrences with constant coefficients, signature (1,10,-10).
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FORMULA
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a(n+2) = 10*a(n) + 1 for n >= 2.
a(2*n) = (10^n - 1)/9 ; a(2*n + 1) = ((10^n - 1)/9) + 6*10^(n - 1).
From Stefano Spezia, Sep 29 2020: (Start)
G.f.: x^2*(1 + 6*x - 6*x^2)/(1 - x - 10*x^2 + 10*x^3).
a(n) = a(n-1) + 10*a(n-2) - 10*a(n-3) for n > 4. (End)
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MATHEMATICA
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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 *)
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CROSSREFS
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Cf. A063720 (number of segments), A216261 (smallest number), A249572.
Sequence in context: A177182 A061809 A289286 * A123763 A018680 A107187
Adjacent sequences: A337096 A337097 A337098 * A337100 A337101 A337102
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KEYWORD
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nonn,base
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AUTHOR
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Suren Suren, Sep 29 2020
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EXTENSIONS
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More terms from Stefano Spezia, Sep 29 2020
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STATUS
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approved
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