Repeating Mod16 Sequences derived from Fibonacci numbers divided into Fibonacci numbers (integer results only) 1 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368 75025 121393 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 Position in Divisor Sequence 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 1 1 2 3 5 8 13 5 2 7 9 16 9 9 1 3 8 5 7 16 9 11 8 13 15 16 1 4 1 8 1 12 1 16 1 7 16 9 15 16 1 11 10 9 13 8 5 15 10 13 9 1 2 3 4 5 6 7 8 9 10 1 13 10 15 13 8 5 9 10 1 15 16 1 12 1 8 1 4 1 1 11 8 13 7 16 1 7 2 5 5 1 2 3 4 1 9 2 1 11 1 Notes of interest 16 17 18 19 20 21 22 23 24 2 11 13 8 5 13 2 15 1 16 24 12 8 6 16 9 3 10 1 5 8 13 7 10 5 1 16 24 11 12 13 14 15 16 16 11 9 16 9 5 10 7 5 8 13 1 10 3 1 16 16 3 16 8 9 3 8 5 15 16 12 8 13 3 2 1 9 16 9 15 2 13 13 8 5 11 2 9 1 16 24 5 6 7 8 9 10 11 12 13 14 15 16 16 11 5 8 13 13 2 15 9 16 9 1 2 3 13 8 5 5 2 7 1 16 24 Same as 11, backwards 8 13 7 16 9 3 8 5 15 16 12 Identical to 10 4 1 8 1 12 1 16 8 Same as 9, backwards 1 15 16 3 Identical to 8 1 3 10 1 13 8 5 7 10 5 9 16 9 11 10 9 5 8 13 15 10 13 1 16 24 Same as 7, backwards 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 16 Identical to 6 1 5 10 7 13 8 5 1 10 3 9 16 9 13 10 15 5 8 13 9 10 11 1 16 24 Same as 5, backwards 1 7 16 9 15 16 6 Identical to 4 1 12 1 8 1 4 1 16 8 Same as 3, backwards 1 3 8 5 7 16 9 11 8 13 15 16 12 Identical to 2 1 15 2 13 5 8 13 11 2 9 9 16 9 7 2 5 13 8 5 3 2 1 1 16 24 Same as 1, backwards 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 16 Identical to 12 1 1 2 3 5 8 13 5 2 7 9 16 9 9 2 11 13 8 5 13 2 15 1 16 24 Identical to 1 1 3 8 5 7 16 9 11 8 13 15 16 12 Identical to 2 No of digits in sequence Sequence no. Fibonacci Divisor Notes: After sequence 24, there is a repetition of the exactly the same series of sequences as at the beginning. So 25 = 1, 26=2 and so on. Therefore the periodicity of the fmod16 group is 24. Sequences 12 and 24 act almost like mirrors. The length of each sequence on either side of each of these is the same, as with successive positions moving away from 12 and 24. However every second sequence between 12 to 24 are backwards versions of their counterpart. Eg. 13 is a backwards 11 and 15 is a backwards 9. And so on. Nexus Keys. There are no NK’s here as none of these sequences have all of the Characteristics of the Nexus Key outlined in the Mod9 ANALYSIS file. A specific VBM style Nexus key would have to have 1 and 15 on either side of the 16, and continue to add up to 16 as we move successive positions away from 16. Therefore the sequences that are 12 digits long have potential; 2 and 10. (14 and 22 are identical). Also sequences 6, 12, 18, and 24. But none of them are double in length of the modulus. 1.
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Repeating Mod16 Sequences derived from Lucas numbers divided into Lucas numbers (integer results only) Lucas Divisor 1 2 1 3 4 7 11 18 29 47 76 123 199 322 521 843 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Position in Divisor Sequence 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 1 2 9 6 1 10 9 14 2 1 3 4 7 11 12 13 15 12 11 7 2 9 1 6 9 6 1 1 3 5 7 9 11 13 15 1 14 1 1 12 3 5 4 7 9 12 11 13 1 1 12 3 5 4 7 9 12 1 14 1 1 3 5 7 9 11 1 6 9 6 1 1 4 11 13 12 1 1 4 11 1 6 9 Notes of interest 16 17 18 19 20 21 22 23 24 8 11 4 15 3 12 5 7 12 3 15 24 5 8 3 4 15 12 1 Line of reflection 11 13 4 15 12 3 13 15 8 5 7 9 4 3 5 12 15 12 1 Line of reflection 13 12 7 9 4 3 5 12 15 12 6 1 5 Repetition of 3 No of digits in sequence Sequence no. 1.
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Notes: As with all other Lucas mod groups S1 and S2 are unique. After S14, there is a repetition of exactly the same series of sequences as from S3 onwards. So S15 = S3, S16=S4 and so on. Therefore the periodicity of the Lmod16 group is 12. S7, S13, S19 and so on are exact mirrors of all sequences on either side of them. Nexus Key absent. No NK sequences here.