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A343184
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Positions of records in A001178.
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0
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1, 2, 127, 509, 1019, 2039, 4079, 16384, 32768, 65536, 131072, 262144, 524287, 1048573, 6291437
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OFFSET
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1,2
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COMMENTS
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When the Pisano-period map x -> A001175(x) is iterated, a(n) is the number of steps needed to reach a fixed point (that is, to reach a term of A235702).
The record values of A001178 at positions 1, 2, 127, 509, 1019, 2039, 4079, 16384, 32768, 65536, 131072, 262144, 524287, 1048573 are 0, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 18, 19.
Felix Lans remarks that from a(4) onwards, the terms appear to be very close to consecutive powers of 2, except that there is no term close to 2^13.
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LINKS
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MATHEMATICA
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Block[{pi, k, s}, pi[1] = 1; pi[n_] := For[k = 1, True, k++, If[Mod[Fibonacci[k], n] == 0 && Mod[Fibonacci[k + 1], n] == 1, Return[k]]]; s = Array[Length[FixedPointList[pi, #]] - 2 &, 2^11]; Map[FirstPosition[s, #][[1]] &, Union@ FoldList[Max, s]] ] (* Michael De Vlieger, May 16 2021, after Jean-François Alcover at A001178 *)
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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