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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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21
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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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refs;
listen;
history;
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internal format)
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OFFSET
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0,1
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COMMENTS
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Characteristic function of A091067.
Image, under the coding i -> floor(i/2), of the fixed point, starting with 0, of the morphism 0 -> 01, 1 -> 02, 2 -> 32, 3 -> 31. - Jeffrey Shallit, May 15 2016
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REFERENCES
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Jean-Paul Allouche and Jeffrey O. Shallit, Automatic sequences, Cambridge, 2003, sect. 5.1.6
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LINKS
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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
Index entries for sequences obtained by enumerating foldings
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FORMULA
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a(0) = 0, a(2*n) = a(n) for n>0, a(4*n+1) = 0, a(4*n+3) = 1.
G.f.: Sum_{k>=0} t^3/(1-t^4), where t=x^2^k. Parity of A025480. a(n) = 1/2 * (1 - (-1)^A025480(n)). - Ralf Stephan, Jan 04 2004
a(n) = 1 if Kronecker(-n,m)=Kronecker(m,n) for all m, otherwise a(n)=0. - Michael Somos, Sep 22 2005
a(n) = 1 iff A164677(n) < 0. - M. F. Hasler, Aug 06 2015
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EXAMPLE
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a(6) = 1 since 6 = 110 and bit before rightmost 1 is a 1.
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MAPLE
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A038189 := proc(n)
option remember;
if n = 0 then
0 ;
elif type(n, 'even') then
procname(n/2) ;
elif modp(n, 4) = 1 then
0 ;
else
1 ;
end if;
end proc:
seq(A038189(n), n=0..100) ; # R. J. Mathar, Mar 30 2018
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MATHEMATICA
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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, fixed Feb 27 2014 *)
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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 */
(PARI) A038189(n)=bittest(n, valuation(n, 2)+1) \\ M. F. Hasler, Aug 06 2015
(PARI) a(n)=my(h=bitand(n, -n)); n=bitand(n, h<<1); n!=0; \\ Joerg Arndt, Apr 09 2021
(Magma)
function a (n)
if n eq 0 then return 0; // alternatively, return 1;
else while IsEven(n) do n := n div 2; end while; end if;
return n div 2 mod 2; end function;
nlo := 0; nhi := 32;
[a(n) : n in [nlo..nhi] ]; // Fred Lunnon, Mar 27 2018
(Python)
def A038189(n):
s = bin(n)[2:]
m = len(s)
i = s[::-1].find('1')
return int(s[m-i-2]) if m-i-2 >= 0 else 0 # Chai Wah Wu, Apr 08 2021
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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
Related sequences A301848, A301849, A301850. - Fred Lunnon, Mar 27 2018
Sequence in context: A288508 A262588 A234577 * A072783 A353478 A353555
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, Dec 11 1999
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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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