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

Author

Arlu Genesis A. Padilla, Jan 14 2015

Keywords

• easy
• nonn
• base

Comments

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:

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Examples

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

Links

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

Crossrefs

Cf. A007088, A010371, A074458.

Programs

C

// 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

Mathematica

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

PARI

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

Python

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

Formula

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