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A263792
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"Shuffled bisection" of positive even and odd numbers, Type 2 (see "Comments" for rules generating the sequence).
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2
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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, 18, 35, 37, 20, 39, 41, 43, 22, 45, 47, 24, 49, 26, 51, 53, 28, 55, 30, 32, 57, 59, 61, 34, 63, 36, 65, 67, 38, 69, 71, 73, 40, 42, 44, 75, 46, 77, 79, 48, 50
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OFFSET
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1,2
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COMMENTS
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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:
Start with a(1)=1; take next odd number until preceding an odd composite, then take next even number. Take next odd unless coprime to last term, otherwise take next even. Repeat indefinitely.
Odd terms precede primes (by definition); primes are followed by even terms unless smallest twin prime.
Excluding a(1)..a(4), the maximum length of odd strings is 3. Is there a limit to the maximum length of even strings?
If seeds are a(1)=1 and a(2)=2, the sequences converge after a(17).
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LINKS
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EXAMPLE
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a(11)=17; since next odd is prime, take a(12)=19. Since next odd is composite, take next even, so a(13)=6. Since next odd (21) is not coprime to 6, take a(14)=8. Since 21 is coprime to 8, take a(15)=21.
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MATHEMATICA
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f[n_] := Block[{a = 3, b = 2, t = {1}, k}, Do[Which[And[OddQ@ t[[k - 1]], PrimeQ@ a], AppendTo[t, a]; a += 2, And[OddQ@ t[[k - 1]], CompositeQ@ a], AppendTo[t, b]; b += 2, And[EvenQ@ t[[k - 1]], CoprimeQ[a, t[[k - 1]]]], AppendTo[t, a]; a += 2, And[EvenQ@ t[[k - 1]], ! CoprimeQ[a, t[[k - 1]]]], AppendTo[t, b]; b += 2, True, AppendTo[t, 1]], {k, 2, n}]; t]; f@ 120 (* Michael De Vlieger, Oct 27 2015 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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