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%I #8 Aug 01 2015 06:09:01
%S 1,3,5,9,13,17,19,27,29,35,43,45,57,59,61,67,81,83,93,99,107,115,123,
%T 125,137,141,149,163,165,173,189,195,201,213,217,219,229,243,249,267,
%U 269,275,283,297,307,313
%N Produced by a sieve: Start with the natural numbers; at the k-th step remove every A138007(k+1)-th term of the sequence remaining after the (k-1)-st sieving step.
%C The sequence A138007 is defined using this sequence, in the same way as A138007 is used to define this sequence.
%C The sequences can be found this way:
%C Define a(n,1)=n.
%C Now write the natural numbers and run this sieve: In the k-th step remove every a(k+1,1)-th number that remained after k-1 step. You will get this:
%C 1, 3, 7, 13, 19, ... (A000960).
%C Now let a(n,2) be n-th number in this sequence.
%C In the same way: Define a(n,i+1) to be the n-th number left after running the similar sieve on the natural numbers using a(n,i) instead of a(n,1). Now:
%C a(n,2i+1)-> A138007(n) when i->infinity and,
%C a(n,2i)-> A138008(n) when i->infinity.
%e Start with the natural numbers:
%e 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, ...
%e Remove every A138007(2)=2nd term:
%e 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, ...
%e Remove every A138007(3)=4th term:
%e 1, 3, 5, 9, 11, 13, 17, 19, ...
%e Remove every A138008(4)=5th term:
%e 1, 3, 5, 9, 13, 17, 19, ...
%e and so on.
%Y Cf. A138007.
%K nonn
%O 1,2
%A Sune Kristian Jakobsen (sunejakobsen(AT)hotmail.com), Feb 27 2008