they are indeed two series merged together , but lets do a little bit fancier thing with it ...it can be considered a single sequence

look at the series as . view it as power of 2

2⁰, 2¹, 2¹, 2⁰, 2¹, 2¹, 2², 2¹, 2³, 2², 2⁵, 2³, 2^{8       <o:p></o:p>}

^{<o:p> </o:p>}

See any catch above ??? look at the powers of  2

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0,1,1,0,1,1,2,1,3,2,5,3,8……

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First + second = third

                           third + fourth = fifth

                                                     fifth + sixth = seventh …… and so on ……

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more interestingly these First , third , fifth , seventh , ninth , and so on values form an interesting sequence ………  the Fibonacci   0 1 1 2  3 5 8 13(the missing fifteenth number of the series is 2¹³)  missing fourteenth number is 2⁵ (because 8+5=13 conforming with our above sequence or 5 can be viewed as Fibonacci predecessor of 8 whatever ya want) . next numbers are

  2¹³,2⁸,2²¹   (fifteenth,sixteenth,seventeenth numbers repectively)

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so the missing numbers are 32, 8192, 256 ....(fourteenth,fifteenth and sixteeenth numbers)

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<o:p> </o:p>

     2⁰, 2¹, 2¹, 2⁰, 2¹, 2¹, 2², 2¹, 2³, 2², 2⁵, 2³, 2⁸ ,2⁵ ,2¹³,2⁸,2^{21<o:p></o:p>}

^{<o:p> </o:p>}

Every three number pairs (1,2,3 or 3,4,5 or 5,6,7  or 7,8,9 shows our fibbonacci sequence)

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Ahahahahahaha ……. complicated the matters ….. actually just read Da Vinci’s Code by Dan Brown …so bit obsessed with fibbonacci ……   you are right Eric ….well done