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A079255 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. 2
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; text; internal format)
OFFSET
1,2
COMMENTS
No two terms in the sequence are consecutive integers (see example for a(3)).
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)
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, Apr 23 2008
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.
CROSSREFS
Cf. A079000, A079259. First differences give A080428.
Sequence in context: A304231 A007074 A054087 * A171845 A157124 A162735
KEYWORD
easy,nonn
AUTHOR
STATUS
approved

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Last modified April 14 16:48 EDT 2024. Contains 371666 sequences. (Running on oeis4.)