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A038189
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Bit to left of least significant 1-bit in binary expansion of n.
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16
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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
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OFFSET
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0,1
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COMMENTS
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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
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LINKS
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Table of n, a(n) for n=0..107.
Michael Gilleland, Some Self-Similar Integer Sequences
Index entries for characteristic functions
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FORMULA
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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
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EXAMPLE
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a(6) = 1 since 6 = 110 and bit before right-most 1 is a 1.
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MATHEMATICA
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f[n_] := IntegerDigits[n, 2][[2]]; f[0] = f[1] = 0; Table[f@n, {n, 0, 104}] [From Robert G. Wilson v, Apr 14 2009]
f[n_] := f[n] = Switch[ Mod[n, 4], 0, g[n/2], 1, 0, 2, g[n/2], 3, 1]; Table[ f@n, {n, 0, 104}] [From Robert G. Wilson v, Apr 14 2009]
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PROG
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(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 */
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CROSSREFS
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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
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KEYWORD
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nonn,easy
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AUTHOR
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Fred Lunnon (fred(AT)csa5.cs.may.ie)
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EXTENSIONS
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More terms from David W. Wilson
Definition corrected by Russ Cox and Ralf Stephan, Nov 08 2004
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STATUS
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approved
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