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A091072
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Numbers a(n) such that odd part of a(n) is of form 4k+1. The bit to the left of least significant bit of a(n) is unset.
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12
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1, 2, 4, 5, 8, 9, 10, 13, 16, 17, 18, 20, 21, 25, 26, 29, 32, 33, 34, 36, 37, 40, 41, 42, 45, 49, 50, 52, 53, 57, 58, 61, 64, 65, 66, 68, 69, 72, 73, 74, 77, 80, 81, 82, 84, 85, 89, 90, 93, 97, 98, 100, 101, 104, 105, 106, 109, 113, 114, 116, 117, 121, 122, 125, 128, 129
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Either of form 2a(m) or 4k+1, k>=0, 0<m<n.
A000265(a(n)) is an element of A016813.
a(n) such that A038189(a(n)) = 0.
Numbers n such that kronecker( n, m) = kronecker( m, n) for all m. - Michael Somos, Sep 24 2005
The Dragon curve A014577 (but changing the offset to 1: (1, 1, 0, 1, 1, 0, 0, 1, 1, 1,...) = the characteristic function of A091072. -- Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 11 2010
A014707(a(n) + 1) = 0. [Reinhard Zumkeller, Sep 28 2011]
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LINKS
| J. E. S. Socolar and J. M. Taylor, An aperiodic hexagonal tile
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
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EXAMPLE
| x + 2*x^2 + 4*x^3 + 5*x^4 + 8*x^5 + 9*x^6 + 10*x^7 + 13*x^8 + 16*x^9 + ...
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MATHEMATICA
| Select[ Range[129], EvenQ[ (#/2^IntegerExponent[#, 2] - 1)/2 ] & ] (* From Jean-François Alcover, Feb 16 2012, after Pari *)
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PROG
| (PARI) for(n=1, 200, if(((n/2^valuation(n, 2)-1)/2)%2==0, print1(n", ")))
(PARI) {a(n) = local(m, c); if( n<1, 0, c=1; m=1; while( c<n, m++; if( ((m / 2^valuation( m, 2) - 1) / 2)%2==0, c++)); m)} /* Michael Somos, Sep 24 2005 */
(Haskell)
import Data.List (elemIndices)
a091072 n = a091072_list !! (n-1)
a091072_list = map (+ 1) $ elemIndices 0 a014707_list
-- Reinhard Zumkeller, Sep 28 2011
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CROSSREFS
| Complement of A091067.
First differences are in A088742.
Cf. A014577 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 11 2010]
Sequence in context: A169612 A084581 A121996 * A001481 A034026 A125022
Adjacent sequences: A091069 A091070 A091071 * A091073 A091074 A091075
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KEYWORD
| nonn,easy,changed
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AUTHOR
| Ralf Stephan (ralf(AT)ark.in-berlin.de), Feb 22 2004
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