A230113 Digital root of summed Fibonacci and Lucas digital roots indexed by numbers not divisible by 2, 3 or 5.
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, 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, 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
Offset: 1
Examples
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.
Formula
Conjectures from Colin Barker, Sep 22 2019: (Start)
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)).
a(n) = a(n-1) - a(n-16) + a(n-17) for n>17.
(End)
Comments