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Let there be a set of increasing order integer data ${a_1, a_2, a_3, a_4, ...}$. given the increasing infinite sequence of integers, how can we determine whether there is an infinite subsequence which is a subsequence of a shifted fibonacci sequence?

Anthony
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  • The sentence in brackets makes no sense. – Gerry Myerson Mar 16 '15 at 09:02
  • Thank you Gerry, I edited it. (I missed the end of the sentence) – Anthony Mar 16 '15 at 09:25
  • I add here some further thoughts which go some way illustrating the problem. If some of the numbers in the data set are the well known fibonacci numbers then the problem is easier as we can apply the test stated in the brackets for each number in the set, then check if the fibonacci identified numbers are successive. However the data could also have 'shifted' fibonacci sequences $F_k +m$ or a mix of shifts $F_k +q$ (m,q integers). – Anthony Mar 16 '15 at 09:35
  • What do you mean by "the index of the number data"? – Gerry Myerson Mar 17 '15 at 05:15
  • Are you still here? – Gerry Myerson Mar 19 '15 at 04:38
  • Sorry I dont live here....I mean we do not know the number k of $F_k$. Why is that? Because number 3 for example could be k=1 of a sequence shifted by 3, ($F_k+3) $, OR , k=4 of $F_k$ – Anthony Mar 20 '15 at 07:03
  • Basically my observable is known as difference in numbers but I do not know on which spiral branch the data belong to. (If you know what I mean) – Anthony Mar 20 '15 at 07:09
  • I have no idea what you mean. I don't see any spirals, for starters. – Gerry Myerson Mar 20 '15 at 08:52
  • I'm still trying to make sense of your question. You aren't helping, much. Is this your question: given an increasing infinite sequence of integers, how can we determine whether there is an infinite subsequence which is a subsequence of a shifted fibonacci sequence? – Gerry Myerson Mar 21 '15 at 22:33
  • Yes this can be described as you say. Thanks... – Anthony Mar 23 '15 at 11:35
  • Good. Then, why don't you edit it so it says that? – Gerry Myerson Mar 23 '15 at 12:05
  • OK IF this helps I have... – Anthony Mar 23 '15 at 12:27

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