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a(n) is difference of indices of terms >= 9 in A187824.
3

%I #49 Jan 25 2013 16:25:21

%S 16,90,55,233,55,1,54,16,56,34,55,1,70,90,128,70,56,34,55,1,70,1,55,

%T 34,56,70,128,90,70,1,55,34,56,16,54,1,55,233,55,90,16,54,1,1,54,16,

%U 90,55,233,55,1,54,16,56,34,55,1,70,90,128,70,56,34,55,1,70

%N a(n) is difference of indices of terms >= 9 in A187824.

%C The repeat cycle contains 45 numbers which have 22 Fibonacci numbers symmetrically distributed as below.

%C 1 F(1), F(2)

%C 54

%C 16

%C 90

%C 55 F(10)

%C 233 F(13)

%C 55 F(10)

%C 1 F(1), F(2)

%C 54

%C 16

%C 56

%C 34 F(9)

%C 55 F(10)

%C 1 F(1), F(2)

%C 70

%C 90

%C 128

%C 70

%C 56

%C 34 F(9)

%C 55 F(10)

%C 1 F(1), F(2)

%C 70

%C 1 F(1), F(2)

%C 55 F(10)

%C 34 F(9)

%C 56

%C 70

%C 128

%C 90

%C 70

%C 1 F(1), F(2)

%C 55 F(10)

%C 34 F(9)

%C 56

%C 16

%C 54

%C 1 F(1), F(2)

%C 55 F(10)

%C 233 F(13)

%C 55 F(10)

%C 90

%C 16

%C 54

%C 1 F(1), F(2)

%e For A187824(m(i)) >= 9:

%e m(1) = 55, m(2) = 71, m(3) = 161, m(4) = 216,

%e ...

%e a(1) = 71 - 55 = 16, a(2) = 161 - 71 = 90,

%e a(3) = 216 - 161 = 55,

%e ...

%t A187824[n_ /; n > 1] := Catch[For[k = 4, True, k++, m = Mod[n, k, -Floor[k/2]]; If[m != m^3, Throw[k - 1]]]]; Differences[Select[Range[2, 6000], A187824[#] >= 9 &] ] (* _Jean-François Alcover_, Jan 09 2013 *)

%o (Small Basic)

%o j = 1

%o For n = 1 To 2000

%o For m = 1 To 100

%o I = Math.Round(n/m)

%o D = Math.Abs(n-I*m)

%o If D > 1 Then

%o a = m - 1

%o Goto OUT

%o Else

%o EndIf

%o EndFor

%o OUT:

%o If a >= 9 Then 'Filter for A187824 >= 9

%o mm[j] = n

%o j = j + 1

%o Else

%o EndIf

%o EndFor

%o For ii = 1 to j

%o aa[ii] = mm[ii+1] - mm[ii]

%o TextWindow.Write(ii+" ")

%o TextWindow.Write(aa[ii]+" ")

%o TextWindow.WriteLine(" ")

%o EndFor

%Y Cf. A187824.

%K nonn

%O 1,1

%A _Kival Ngaokrajang_, Dec 31 2012