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A249919 Number of LCD (liquid-crystal display) segments needed to display n in binary. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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:

   _

  | |        |

  |_|  and   |

LINKS

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

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

EXAMPLE

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

MATHEMATICA

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

PROG

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

(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

(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

CROSSREFS

Cf. A007088, A010371, A074458.

Sequence in context: A098686 A079718 A062771 * A254868 A071874 A011331

Adjacent sequences:  A249916 A249917 A249918 * A249920 A249921 A249922

KEYWORD

easy,nonn,base

AUTHOR

Arlu Genesis A. Padilla, Jan 14 2015

STATUS

approved

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Last modified February 27 11:19 EST 2021. Contains 341653 sequences. (Running on oeis4.)