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A168160 Number of 0's in the matrix whose lines are the binary expansion of the numbers 1,...,n. 1
0, 2, 2, 7, 8, 9, 9, 19, 21, 23, 24, 26, 27, 28, 28, 47, 50, 53, 55, 58, 60, 62, 63, 66, 68, 70, 71, 73, 74, 75, 75, 111, 115, 119, 122, 126, 129, 132, 134, 138, 141, 144, 146, 149, 151, 153, 154, 158, 161, 164, 166, 169, 171, 173, 174, 177, 179, 181, 182, 184, 185, 186 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The matrix is to be taken of minimal size, i.e., have n lines and the number of columns needed to write n in base 2 in the last line, A070939(n). Otherwise said, there is no zero column.

The number of zeros in the last line of the matrix is given by A023416(n).

One has a(n)=a(n-1) iff n = 2^k-1 for some k.

LINKS

Table of n, a(n) for n=1..62.

FORMULA

A168160(n)=n*A070939(n)-A000788(n).

EXAMPLE

a(4)=7 is the number of zeros in the matrix

[001] /* = 1 in binary */

[010] /* = 2 in binary */

[011] /* = 3 in binary */

[100] /* = 4 in binary */

PROG

(PARI) A168160(n)=n*#binary(n)-sum(i=1, n, norml2(binary(i)))

CROSSREFS

Cf. A059015.

Sequence in context: A151864 A019732 A199467 * A005300 A019087 A293607

Adjacent sequences:  A168157 A168158 A168159 * A168161 A168162 A168163

KEYWORD

base,nonn

AUTHOR

M. F. Hasler, Nov 22 2009

STATUS

approved

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Last modified October 18 20:42 EDT 2019. Contains 328197 sequences. (Running on oeis4.)