A337099 Largest positive number using exactly n segments on a calculator display (when '6' and '7' are represented using 6 resp. 3 segments).

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

Offset: 2

Author

Suren Suren, Sep 29 2020

Keywords

• nonn
• base

Comments

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.

Links

• Index entries for sequences related to calculator display
• Index entries for linear recurrences with constant coefficients, signature (1,10,-10).

Crossrefs

Cf. A063720 (number of segments), A216261 (smallest number), A249572.

Programs

Mathematica

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 *)

Formula

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)

Extensions

More terms from Stefano Spezia, Sep 29 2020