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A192129 a(n) is difference of indices of terms >= 9 in A187824.

%I A192129 #49 Jan 25 2013 16:25:21
%S A192129 16,90,55,233,55,1,54,16,56,34,55,1,70,90,128,70,56,34,55,1,70,1,55,
%T A192129 34,56,70,128,90,70,1,55,34,56,16,54,1,55,233,55,90,16,54,1,1,54,16,
%U A192129 90,55,233,55,1,54,16,56,34,55,1,70,90,128,70,56,34,55,1,70
%N A192129 a(n) is difference of indices of terms >= 9 in A187824.
%C A192129 The repeat cycle contains 45 numbers which have 22 Fibonacci numbers symmetrically distributed as below.
%C A192129 1      F(1), F(2)
%C A192129 54
%C A192129 16
%C A192129 90
%C A192129 55     F(10)
%C A192129 233    F(13)
%C A192129 55     F(10)
%C A192129 1      F(1), F(2)
%C A192129 54
%C A192129 16
%C A192129 56
%C A192129 34     F(9)
%C A192129 55     F(10)
%C A192129 1      F(1), F(2)
%C A192129 70
%C A192129 90
%C A192129 128
%C A192129 70
%C A192129 56
%C A192129 34     F(9)
%C A192129 55     F(10)
%C A192129 1      F(1), F(2)
%C A192129 70
%C A192129 1      F(1), F(2)
%C A192129 55     F(10)
%C A192129 34     F(9)
%C A192129 56
%C A192129 70
%C A192129 128
%C A192129 90
%C A192129 70
%C A192129 1      F(1), F(2)
%C A192129 55     F(10)
%C A192129 34     F(9)
%C A192129 56
%C A192129 16
%C A192129 54
%C A192129 1      F(1), F(2)
%C A192129 55     F(10)
%C A192129 233    F(13)
%C A192129 55     F(10)
%C A192129 90
%C A192129 16
%C A192129 54
%C A192129 1      F(1), F(2)
%e A192129 For A187824(m(i)) >= 9:
%e A192129 m(1) = 55, m(2) = 71, m(3) = 161, m(4) = 216,
%e A192129 ...
%e A192129 a(1) = 71 - 55 = 16, a(2) = 161 - 71 = 90,
%e A192129 a(3) = 216 - 161 = 55,
%e A192129 ...
%t A192129 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 A192129 (Small Basic)
%o A192129 j = 1
%o A192129 For n = 1 To 2000
%o A192129   For m = 1 To 100
%o A192129   I = Math.Round(n/m)
%o A192129   D = Math.Abs(n-I*m)
%o A192129   If D > 1 Then
%o A192129     a = m - 1
%o A192129         Goto OUT
%o A192129    Else
%o A192129    EndIf
%o A192129   EndFor
%o A192129   OUT:
%o A192129   If a >= 9 Then 'Filter for A187824 >= 9
%o A192129     mm[j] = n
%o A192129     j = j + 1
%o A192129    Else
%o A192129   EndIf
%o A192129 EndFor
%o A192129 For ii = 1 to j
%o A192129    aa[ii] = mm[ii+1] - mm[ii]
%o A192129    TextWindow.Write(ii+" ")
%o A192129    TextWindow.Write(aa[ii]+" ")
%o A192129    TextWindow.WriteLine(" ")
%o A192129 EndFor
%Y A192129 Cf. A187824.
%K A192129 nonn
%O A192129 1,1
%A A192129 _Kival Ngaokrajang_, Dec 31 2012