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A038189 Bit to left of least significant 1-bit in binary expansion of n. 16
0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Characteristic function of A091067.

a(n)=1 if kronecker(-n,m)=kronecker(m,n) for all m, otherwise a(n)=0. - Michael Somos, Sep 22 2005

LINKS

Ivan Panchenko, Table of n, a(n) for n = 0..10000

Michael Gilleland, Some Self-Similar Integer Sequences

Index entries for characteristic functions

Index entries for sequences related to binary expansion of n

FORMULA

a(0) = 0, a(2n) = a(n) for n>0, a(4n+1) = 0, a(4n+3) = 1.

G.f.: sum (k>=0, t^3/(1-t^4), t=x^2^k). Parity of A025480. a(n) = 1/2 * (1 - (-1)^A025480(n)). - Ralf Stephan, Jan 04 2004

EXAMPLE

a(6) = 1 since 6 = 110 and bit before rightmost 1 is a 1.

MATHEMATICA

f[n_] := Block[{id2 = Join[{0}, IntegerDigits[n, 2]]}, While[ id2[[-1]] == 0, id2 = Most@ id2]; id2[[-2]]]; f[0] = 0; Array[f, 105, 0] (* Robert G. Wilson v, Apr 14 2009 and fixed Feb 27 2014 *)

f[n_] := f[n] = Switch[Mod[n, 4], 0, f[n/2], 1, 0, 2, f[n/2], 3, 1]; f[0] = 0; Array[f, 105, 0] (* Robert G. Wilson v, Apr 14 2009 and fixed Feb 27 2014 *)

PROG

(C) int a(int n) { return (n & ((n&-n)<<1)) ? 1 : 0; } /* from Russ Cox */

(PARI) a(n) = if(n<1, 0, ((n/2^valuation(n, 2)-1)/2)%2) /* Michael Somos, Sep 22 2005 */

(PARI) a(n) = if(n<3, 0, prod(m=1, n, kronecker(-n, m)==kronecker(m, n))) /* Michael Somos, Sep 22 2005 */

CROSSREFS

Cf. A038190.

A014707(n)=a(n+1). A014577(n)=1-a(n+1).

The following are all essentially the same sequence: A014577, A014707, A014709, A014710, A034947, A038189, A082410. - N. J. A. Sloane, Jul 27 2012

Sequence in context: A100283 A134391 A102215 * A072783 A064911 A174898

Adjacent sequences:  A038186 A038187 A038188 * A038190 A038191 A038192

KEYWORD

nonn,easy

AUTHOR

Fred Lunnon, Dec 11 1999

EXTENSIONS

More terms from David W. Wilson

Definition corrected by Russ Cox and Ralf Stephan, Nov 08 2004

STATUS

approved

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Last modified October 22 06:47 EDT 2014. Contains 248388 sequences.