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A205866 Positions of multiples of 8 in A204922 (differences of Fibonacci numbers).

%I A205866 #14 Jul 28 2020 07:01:30
%S A205866 14,19,21,23,37,50,56,65,67,76,78,80,86,94,109,111,112,125,131,140,
%T A205866 142,143,152,157,159,160,169,171,173,179,185,199,211,220,222,223,236,
%U A205866 242,248,254,263,265,266,275,277,286,288,289,298,300,302,308,314
%N A205866 Positions of multiples of 8 in A204922 (differences of Fibonacci numbers).
%C A205866 For a guide to related sequences, see A205840.
%H A205866 Robert Israel, <a href="/A205866/b205866.txt">Table of n, a(n) for n = 1..10000</a>
%e A205866 In A204922=(1,2,1,4,3,2,7,6,5,3,12,11,...), multiples of 8 are in positions 14,19,21,...  See the example at A205867.
%p A205866 R:= select(t -> combinat:-fibonacci(t[1])-combinat:-fibonacci(t[2]) mod 8 =0, [seq(seq([i,j],i=0..11),j=0..11)]):
%p A205866 Res:= NULL:
%p A205866 for kk from 3 to 50 do
%p A205866    km:= kk mod 12;
%p A205866    n0:= 1 + (kk-2)*(kk-3)/2;
%p A205866    js:= [$n0 ..(n0+kk-3)];
%p A205866    Res:= Res, op( select(t -> member([kk, t+2-n0] mod 12,R), js));
%p A205866 od:
%p A205866 Res; # _Robert Israel_, Jul 27 2020
%t A205866 (See the program at A205867.)
%Y A205866 Cf. A204890, A205867, A205840.
%K A205866 nonn
%O A205866 1,1
%A A205866 _Clark Kimberling_, Feb 02 2012