%I #21 Sep 08 2022 08:46:14
%S 1,2,13,25,31,43,55,61,73,85,91,103,115,121,133,145,151,163,175,181,
%T 193,205,211,223,235,241,253,265,271,283,295,301,313,325,331,343,355,
%U 361,373,385,391,403,415,421,433,445,451,463,475,481,493,505,511,523,535,541,553
%N Integers k such that A098531(k) is divisible by A000071(k+2).
%C Sequence is interesting because of the values of a(n) - a(n-1) that are 12 or 6 for n > 3.
%C a(2) = 2 is the only even term.
%H Colin Barker, <a href="/A263537/b263537.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1).
%F From _Colin Barker_, Oct 20 2015: (Start)
%F a(n) = a(n-1)+a(n-3)-a(n-4) for n>6.
%F G.f.: x*(x^5+5*x^4+11*x^3+11*x^2+x+1) / ((x-1)^2*(x^2+x+1)).
%F (End)
%e a(1) = 1 because 1^5 mod 1 = 0.
%e a(2) = 2 because (1^5 + 1^5) mod (1 + 1) = 0.
%t lim = 560; s = Accumulate[Fibonacci[Range@lim]^5]; t = Fibonacci@ Range[2 lim] - 1; Select[Range@ lim, Divisible[s[[#]], t[[# + 2]]] &] (* _Michael De Vlieger_, Nov 19 2015, after _Harvey P. Dale_ at A098531 and A000071 *)
%o (PARI) for(n=1, 1e3, if(sum(k=1, n, fibonacci(k)^5) % sum(k=1, n, fibonacci(k)) == 0, print1(n", ")));
%o (PARI) Vec(x*(x^5+5*x^4+11*x^3+11*x^2+x+1)/((x-1)^2*(x^2+x+1)) + O(x^100)) \\ _Colin Barker_, Oct 20 2015
%o (Magma) I:=[1,2,13,25,31,43]; [n le 6 select I[n] else Self(n-1)+Self(n-3)-Self(n-4): n in [1..60]]; // _Vincenzo Librandi_, Nov 20 2015
%Y Cf. A000045, A000071, A098531.
%K nonn,easy
%O 1,2
%A _Altug Alkan_, Oct 20 2015