A010371 -id:A010371 - cp's OEIS frontend

A249919 Number of LCD (liquid-crystal display) segments needed to display n in binary.

6, 2, 8, 4, 14, 10, 10, 6, 20, 16, 16, 12, 16, 12, 12, 8, 26, 22, 22, 18, 22, 18, 18, 14, 22, 18, 18, 14, 18, 14, 14, 10, 32, 28, 28, 24, 28, 24, 24, 20, 28, 24, 24, 20, 24, 20, 20, 16, 28, 24, 24, 20, 24, 20, 20, 16, 24, 20, 20, 16, 20, 16, 16, 12, 38, 34, 34, 30, 34, 30, 30, 26, 34, 30, 30, 26, 30, 26, 26

Offset: 0

Arlu Genesis A. Padilla, Jan 14 2015

The "LCD" refers to how 0 and 1 are displayed, such that zero is represented with 6 lines, and one is represented with 2 lines:
   _
  | |        |
  |_|  and   |

			For n = 4, 4 = 100_2. So, a(4) = 2 + 6 + 6 = 14. - _Indranil Ghosh_, Feb 02 2017

Indranil Ghosh, Table of n, a(n) for n = 0..32768

Cf. A007088, A010371, A074458.

// Input: n (no negative offset/term number), Output: a(n)
int A249919 (int n) {
   int m=0, r=0;
   if (n) {
      while (n!=1) {
         m=n&1; //equivalent to m=n%2;
         n=n>>1; //equivalent to n/=2;
         if (m) {
            r+=2;
         } else {
            r+=6;
         }
      }
      r+=2;
   } else {
      r+=6;
   }
   return r;
}
// Arlu Genesis A. Padilla, Jun 18 2015

f[n_] := Total[{2, 6}*(Count[ IntegerDigits[n, 2], #] & /@ {1, 0})]; Array[f, 79, 0] (* Robert G. Wilson v, Jul 26 2015 *)

a(n)=if(n==0, 6, 6*#binary(n) - 4*hammingweight(n)); \\ Charles R Greathouse IV, Feb 28 2015

def A249919(n):
    x=bin(n)[2:]
    s=0
    for i in x:
        s+=[6,2][int(i)]
    return s # Indranil Ghosh, Feb 02 2017

The formulas below do not include a(0)=6:
a(2^(n-1)) = 2 + 6(n-1).
a((2^n)-1) = 2n.
a(x) = a(2^(n+1) + (2^n)-1) = a(2^(n+2)-1) + 4.
a(y) = a(2^(n+1) + (2^n)) = a(2^(n+1)) - 4.
a(x - u) + 6 = a(x - u + 2^(n+1)).
a(y + u) + 6 = a(y + u + 2^(n+1)).
a(2^(n+1)) + a(2^(n+2)-1) = a(x - u) + a(y + u).
where n=1, 2, ...
and u=0, ..., (2^n)-2.
a(n) = A010371(A007088(n)). - Michel Marcus, Aug 01 2015

A387106 Number of iterations of seven segments count x -> A074458(x) to go from n to a fixed point.

Original entry on oeis.org

1, 2, 1, 1, 0, 0, 0, 1, 2, 1, 3, 1, 2, 2, 1, 2, 3, 1, 2, 2, 2, 2, 4, 4, 2, 4, 2, 2, 3, 4, 2, 2, 4, 4, 2, 4, 2, 2, 3, 4, 4, 1, 2, 2, 3, 2, 4, 3, 2, 2, 2, 2, 4, 4, 2, 4, 2, 2, 3, 4, 3, 3, 2, 2, 4, 2, 3, 4, 3, 2, 4, 1, 2, 2, 3, 2, 4, 3, 2, 2, 3, 2, 3, 3, 2, 3, 3

Offset: 0

Marco Ripà, Aug 16 2025

A074458 is a strictly decreasing function A063720(x) < x whenever x >= 10 and all single digit x reach a fixed point A063720(x) = x with x in {4, 5}.

This sequence is unbounded and the first occurrence of a(n) = k is at n = A338255(k + 2) for any k >= 3.

			For n = 10, the a(10) = 3 steps are 10 -> 8 -> 7 -> 4 segments, and 4 is a fixed point A074458(4) = 4.

Wikipedia, Seven-segment display.

Cf. A074458, A328330, A385249, A386910.

Cf. A006942, A010371, A063720, A277116 (segments variation).

A309721 Number of right angles between the segments that are turned "on" when representing n on a 7-segment (calculator) display.

Original entry on oeis.org

4, 0, 4, 4, 3, 4, 6, 1, 8, 6, 4, 0, 4, 4, 3, 4, 6, 1, 8, 6, 8, 4, 8, 8, 7, 8, 10, 5, 12, 10, 8, 4, 8, 8, 7, 8, 10, 5, 12, 10, 7, 3, 7, 7, 6, 7, 9, 4, 11, 9, 8, 4, 8, 8, 7, 8, 10, 5, 12, 10, 10, 6, 10, 10, 9, 10, 12, 7, 14, 12, 5, 1, 5, 5, 4, 5, 7, 2, 9, 7, 12, 8, 12, 12, 11, 12, 14, 9, 16, 14, 10, 6, 10, 10, 9, 10, 12, 7

Offset: 0

Ivan N. Ianakiev, Aug 14 2019

The display is the one described in A006942 (see also the example section below).

			To illustrate a(0),...,a(9):
   _     _  _       _   _   _   _   _
  | | |  _| _| |_| |_  |_    | |_| |_|
  |_| | |_  _|   |  _| |_|   | |_|  _|
.

Cf. A006942, A010371, A063720, A277116.

Evaluate[Table[a[n],{n,0,9}]]={4,0,4,4,3,4,6,1,8,6};
a[n_/;n>9]:=a[Floor[n/10]]+a[Mod[n,10]]; a/@Range[0,100] (* or *)
Table[Total[IntegerDigits[n]/.{0->4,1->0,2->4,3->4,4-> 3,5->4,7->1,9->6}],{n,0,100}]

a(n) = a(floor(n/10)) + a(n mod 10), for n > 9 (a formula by Reinhard Zumkeller, same for A006942 and A010371).

A386244 Number of iterations of seven segments count x -> A277116(x) to go from n to a fixed point.

Original entry on oeis.org

1, 2, 1, 1, 0, 0, 0, 2, 3, 1, 4, 1, 3, 3, 1, 3, 4, 1, 2, 3, 2, 3, 5, 5, 2, 5, 2, 4, 4, 5, 2, 3, 5, 5, 2, 5, 2, 4, 4, 5, 5, 1, 2, 2, 4, 2, 5, 3, 2, 2, 2, 3, 5, 5, 2, 5, 2, 4, 4, 5, 4, 4, 2, 2, 5, 2, 4, 2, 4, 2, 2, 1, 4, 4, 3, 4, 2, 1, 5, 4, 4, 2, 4, 4, 2, 4, 4, 5, 2, 4

Offset: 0

Marco Ripà, Aug 21 2025

A277116 a strictly decreasing function A277116(x) < x whenever x >= 10 and all single digit x reach a fixed point A277116(x) = x with x in {4, 5, 6}.

This sequence is unbounded and the first occurrence of a(n) = k is at n = A338255(k + 1) for any k >= 3.

			For n = 10, the a(10) = 3 steps are 10 -> 8 -> 7 -> 3 -> 5 segments, and 5 is a fixed point A074458(5) = 5.

Wikipedia, Seven-segment display.

Cf. A277116, A328330, A385249, A386910, A387106.

Cf. A006942, A010371, A063720, A074458 (segments variation).

cp's OEIS Frontend

A249919 Number of LCD (liquid-crystal display) segments needed to display n in binary.

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A387106 Number of iterations of seven segments count x -> A074458(x) to go from n to a fixed point.

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A309721 Number of right angles between the segments that are turned "on" when representing n on a 7-segment (calculator) display.

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A386244 Number of iterations of seven segments count x -> A277116(x) to go from n to a fixed point.

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