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A079255
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a(n) is taken to be the smallest positive integer greater than a(n-1) such that the condition "n is in the sequence if and only if a(n) is odd and a(n+1) is even" can be satisfied.
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2
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1, 4, 6, 9, 12, 15, 18, 20, 23, 26, 28, 31, 34, 36, 39, 42, 44, 47, 50, 53, 56, 58, 61, 64, 66, 69, 72, 75, 78, 80, 83, 86, 88, 91, 94, 97, 100, 102, 105, 108, 110, 113, 116, 119, 122, 124, 127, 130, 132, 135, 138, 140, 143, 146, 148, 151, 154, 157, 160, 162, 165, 168
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| No two terms in the sequence are consecutive integers (see example for a(3)).
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LINKS
| B. Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence, J. Integer Seqs., Vol. 6 (2003), #03.2.2.
B. Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence (math.NT/0305308)
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FORMULA
| With the convention A026363(0)=0 (offset is 1 for this sequence) we have a(n)=A026363(2n)+1; a(n)=(1+sqrt(3))*n+O(1). The sequence satisfies the meta-system for n>=2: a(a(n))=2*a(n)+2*n+2 ; a(a(n)-1)=2*a(n)+2*n-1 ; a(a(n)-2)=2*a(n)+2*n-4 which allows us to have all terms since first differences =2 or 3 only. a(n)=a(n-1)+3 if n is in A026363, a(n)=a(n-1)+2 otherwise (if n is in A026364). - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 23 2008
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EXAMPLE
| a(2) cannot be odd; it also cannot be 2, since that would imply that a(2) was odd. 4 is the smallest value for a(2) that creates no contradiction. a(3) cannot be 5, which would imply that a(5) was odd because it is known from 4's being in the sequence that a(4) is odd and a(5) even. 6 is the smallest value for a(3) that creates no contradiction.
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CROSSREFS
| Cf. A079000, A079259. First differences give A080428.
Cf. A026363, A080428.
Sequence in context: A094202 A007074 A054087 * A171845 A157124 A162735
Adjacent sequences: A079252 A079253 A079254 * A079256 A079257 A079258
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KEYWORD
| easy,nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com) and Matthew Vandermast (ghodges14(AT)comcast.net), Feb 04 2003
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