A230113 - OEIS

%I #14 Sep 22 2019 12:19:44

%S 3,4,5,6,6,5,4,3,4,6,6,5,4,3,3,5,6,5,4,3,3,4,5,6,5,3,3,4,5,6,6,4,3,4,

%T 5,6,6,5,4,3,4,6,6,5,4,3,3,5,6,5,4,3,3,4,5,6,5,3,3,4,5,6,6,4,3,4,5,6,

%U 6,5,4,3,4,6,6,5,4,3,3,5,6,5,4,3,3,4,5,6,5,3,3,4,5,6,6,4

%N Digital root of summed Fibonacci and Lucas digital roots indexed by numbers not divisible by 2, 3 or 5.

%C 32-beat repeating sequence is periodically palindromic starting at Length(40), then at Lengths (72)...(104)...(136)...(168)...{+32 terms ... repeat ... n}.

%F Conjectures from _Colin Barker_, Sep 22 2019: (Start)

%F G.f.: x*(3 + x + x^2 + x^3 - x^5 - x^6 - x^7 + x^8 + 2*x^9 - x^11 - x^12 - x^13 + 2*x^15 + 4*x^16) / ((1 - x)*(1 + x^16)).

%F a(n) = a(n-1) - a(n-16) + a(n-17) for n>17.

%F (End)

%e Referencing A227896 (Fibo) and A233766 (Lucas): 1st Fibo term (1) + 1st Lucas term (2) = 3 = digital root 3. Likewise, 2nd Fibo term (4) + 2nd Lucas term (9) = 13 = digital root 4.

%Y Cf. A007775, A227896, A233766, A000032, A000033.

%K nonn,base,less

%O 1,1

%A _Gary Croft_, Dec 20 2013