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A129760 Bitwise AND of binary representation of n-1 and n. 13
0, 0, 2, 0, 4, 4, 6, 0, 8, 8, 10, 8, 12, 12, 14, 0, 16, 16, 18, 16, 20, 20, 22, 16, 24, 24, 26, 24, 28, 28, 30, 0, 32, 32, 34, 32, 36, 36, 38, 32, 40, 40, 42, 40, 44, 44, 46, 32, 48, 48, 50, 48, 52, 52, 54, 48, 56, 56, 58, 56, 60, 60, 62, 0, 64, 64, 66, 64, 68, 68, 70, 64, 72, 72, 74 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Also the number of Ducci sequences with period n.

Also largest number less than n having in binary representation fewer ones than n has; A048881(n-1) = A000120(a(n)) = A000120(n)-1. - Reinhard Zumkeller, Jun 30 2010

LINKS

R. Zumkeller, Table of n, a(n) for n = 1..10000

R. Brown and J. L. Merzel, The number of Ducci sequences with a given period, Fib. Quart., 45 (2007), 115-121.

FORMULA

a(n) = n AND n-1

Equals n - A006519(n). - N. J. A. Sloane, May 26 2008

From Johannes W. Meijer, Jun 22 2011: (Start)

a((2*n-1)*2^p) = (2*n-2)*(2^p), p>=0.

a(2*n-1) = (2*n-2), n>=1, and a(2^p+1) = 2^p, p>=1. (End)

EXAMPLE

a(6) = 6 AND 5 = binary 110 AND 101 = binary 100 = 4.

MAPLE

nmax := 75: for p from 0 to ceil(simplify(log[2](nmax))) do for n from 1 to ceil(nmax/(p+2)) do a((2*n-1)*2^p) := (2*n-2) * 2^p od: od: seq(a(n), n=1..nmax); # Johannes W. Meijer, Jun 22 2011, revised Jan 25 2013

MATHEMATICA

Table[BitAnd[n, n - 1], {n, 1, 100}] (* Vladimir Joseph Stephan Orlovsky, Jul 19 2011 *)

PROG

(C) int a(int n) { return n & (n-1); }

(PARI) a(n)=bitand(n, n-1) \\ Charles R Greathouse IV, Jun 23 2011

CROSSREFS

Cf. A038712, A086799, A104594, A059991, A006519, A109168, A220466.

Sequence in context: A316987 A228885 A166085 * A291330 A057377 A145811

Adjacent sequences:  A129757 A129758 A129759 * A129761 A129762 A129763

KEYWORD

easy,nonn,hear,base

AUTHOR

Russ Cox, May 15 2007

STATUS

approved

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Last modified October 16 11:25 EDT 2018. Contains 316263 sequences. (Running on oeis4.)