

A079255


a(n) is taken to be the smallest positive integer greater than a(n1) 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
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OFFSET

1,2


COMMENTS

No two terms in the sequence are consecutive integers (see example for a(3)).


LINKS



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 metasystem for n>=2: a(a(n))=2*a(n)+2*n+2 ; a(a(n)1)=2*a(n)+2*n1 ; a(a(n)2)=2*a(n)+2*n4 which allows us to have all terms since first differences =2 or 3 only. a(n)=a(n1)+3 if n is in A026363, a(n)=a(n1)+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



KEYWORD

easy,nonn


AUTHOR



STATUS

approved



