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Search: id:A097581
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| A097581 |
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a(1)=2 then if n even a(n)=a(n-1)+2 and if n odd a(n)=a(n-2)+a(n-1)-1. |
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| 2, 4, 5, 7, 11, 13, 23, 25, 47, 49, 95, 97, 191, 193, 383, 385, 767, 769, 1535, 1537, 3071, 3073, 6143, 6145, 12287, 12289, 24575, 24577, 49151, 49153, 98303, 98305, 196607, 196609, 393215, 393217, 786431, 786433, 1572863, 1572865
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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This sequence a(n)=A016116(n-1)+A086341(n). Generalization: starting with a(1) even then if n even a(n)=a(n-1)+2 and if n odd a(n)=a(n-2)+a(n-1)-1 you get a new sequence as a(1) increases But if a(1) is odd you get always the same sequence with only less values as a(1) increases If a(1) even the sequence difference between two sequences with different but consecutive a(1) is the sequence of powers of 2 = 2,2,4,4,8,8,16,16,32,32,......
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FORMULA
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a(n) = -a(n-1)+2*a(n-2)+2*a(n-3). G.f.: x*(2+6*x+5*x^2)/((1+x)*(1-2*x^2)). [R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 13 2009]
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EXAMPLE
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Starting with a(1)=4 the new sequence is 4,6,9,11,19,21,39,41,79,81,159,161
The sequence difference between sequence starting with a(1)=4 and the sequence starting with a(1)=2 is 2,2,4,4,8,8,16,16,32,32,64,64,.......
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CROSSREFS
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Cf. A016116, A086341.
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KEYWORD
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nonn,new
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AUTHOR
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Pierre CAMI (pierrecami(AT)tele2.fr), Sep 20 2004
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EXTENSIONS
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Equation in the comment corrected by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 13 2009
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