

A249919


Number of LCD (liquidcrystal 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
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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^(n1)) = 2 + 6(n1).
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



