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%I #50 Mar 11 2017 21:12:56
%S 1,3,5,7,2,9,11,13,4,15,17,19,6,8,21,23,10,12,25,14,27,29,31,16,33,35,
%T 37,18,20,39,41,43,22,45,47,24,49,26,51,53,28,55,57,59,61,30,32,63,34,
%U 65,67,36,38,69,71,73,40,42,44,75,46,77,79,48,50
%N "Shuffled bisection" of positive even and odd numbers, type 1 (see "Comments" for rules generating the sequence).
%C All terms are positive, with even and odd terms appearing in due course in order. One might think of the sequence as the result of two poorly-shuffled decks of cards with numbers in increasing order -- one deck with all the positive even numbers and one with all the positive odd numbers, following this set of rules:
%C Start with a(1)=1; take next odd number until preceding an odd composite; then take next even number if coprime to last term, otherwise take next odd. If even term is selected, take next odd unless coprime to last term, otherwise take next even. Repeat indefinitely.
%C Odd terms precede primes (by definition); primes are followed by even terms unless smallest twin prime.
%C Is there a limit to the maximum length of odd or even strings?
%C Same as A263792(n), n <= 25.
%C If seeds are a(1)=1 and a(2)=2, the sequences converge after a(17).
%e a(7)=11; since next odd is prime, take a(8)=13. Since next odd is composite and next even (4) is coprime to 13, take a(9)=4.
%e a(24)=16; since next odd (33) is coprime to 16, take a(25)=33. Since next odd is composite we consider next even (18) as next term; but since 18 is not coprime to 33, instead we take a(26)=35.
%Y Cf. A005408, A005843, A263792.
%K nonn
%O 1,2
%A _Bob Selcoe_, Oct 26 2015
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