Search: id:A038189
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%I A038189
%S A038189 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,
%T A038189 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,
%U A038189 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
%N A038189 Bit to left of least significant 1-bit in binary expansion of n.
%C A038189 Characteristic function of A091067.
%C A038189 a(n)=1 if kronecker(-n,m)=kronecker(m,n) for all m, otherwise a(n)=0. 
               - Michael Somos Sep 22 2005
%H A038189 <a href="Sindx_Ch.html#char_fns">Index entries for characteristic functions</
               a>
%H A038189 Michael Gilleland, <a href="selfsimilar.html">Some Self-Similar Integer 
               Sequences</a>
%F A038189 a(0) = 0, a(2n) = a(n) for n>0, a(4n+1) = 0, a(4n+3) = 1.
%F A038189 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 (ralf(AT)ark.in-berlin.de), 
               Jan 04 2004
%e A038189 a(6) = 1 since 6 = 110 and bit before right-most 1 is a 1.
%t A038189 f[n_] := IntegerDigits[n, 2][[2]]; f[0] = f[1] = 0; Table[f@n, {n, 0, 
               104}] [From Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 14 2009]
%t A038189 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 (rgwv(AT)rgwv.com), 
               Apr 14 2009]
%o A038189 (C) int a(int n) { return (n & ((n&-n)<<1)) ? 1 : 0; } - from Russ Cox
%o A038189 (PARI) a(n) = if(n<1, 0, ((n/2^valuation(n,2)-1)/2)%2) /* Michael Somos 
               Sep 22 2005 */
%o A038189 (PARI) a(n) = if(n<3, 0, prod(m=1,n, kronecker(-n,m)==kronecker(m,n))) 
               /* Michael Somos Sep 22 2005 */
%Y A038189 Cf. A038190.
%Y A038189 A014707(n)=a(n+1). A014577(n)=1-a(n+1).
%Y A038189 A038189(n)=A014707(n-1). [From Robert G. Wilson v (rgwv(AT)rgwv.com), 
               Apr 14 2009]
%Y A038189 Sequence in context: A100283 A064990 A102215 this_sequence A072783 A064911 
               A099618
%Y A038189 Adjacent sequences: A038186 A038187 A038188 this_sequence A038190 A038191 
               A038192
%K A038189 nonn,easy
%O A038189 0,1
%A A038189 Fred Lunnon (fred(AT)csa5.cs.may.ie)
%E A038189 More terms from David W. Wilson (davidwwilson(AT)comcast.net)
%E A038189 Definition corrected by Russ Cox and Ralf Stephan, Nov 08 2004

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