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

Author

Gary Croft, Dec 20 2013

Keywords

• nonn
• base
• less

Comments

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

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.
		

Crossrefs

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

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)