A235944 Digital roots of squares of Lucas numbers.

4, 1, 9, 7, 4, 4, 9, 4, 4, 7, 9, 1, 4, 1, 9, 7, 4, 4, 9, 4, 4, 7, 9, 1, 4, 1, 9, 7, 4, 4, 9, 4, 4, 7, 9, 1, 4, 1, 9, 7, 4, 4, 9, 4, 4, 7, 9, 1, 4, 1, 9, 7, 4, 4, 9, 4, 4, 7, 9, 1, 4, 1, 9, 7, 4, 4, 9, 4, 4, 7, 9, 1, 4, 1, 9, 7, 4, 4, 9, 4, 4, 7, 9, 1, 4, 1, 9, 7, 4, 4, 9, 4, 4, 7, 9, 1, 4, 1, 9, 7, 4, 4, 9, 4, 4, 7, 9, 1

Offset: 0

Author

Colin Barker, Jan 17 2014

Keywords

• nonn
• easy
• base

Comments

The sequence is periodic with period 12.

Examples

			a(5)=4 because A000032[5]=11 and the digital root of 11*11 = 121 is 4.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).

Crossrefs

Cf. A000032, A001254, A216676.

Programs

Mathematica

LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1},{4, 1, 9, 7, 4, 4, 9, 4, 4, 7, 9, 1},108] (* Ray Chandler, Aug 27 2015 *)
PadRight[{},120,{4,1,9,7,4,4,9,4,4,7,9,1}] (* Harvey P. Dale, Feb 18 2018 *)

PARI

Vec(-(x^11+9*x^10+7*x^9+4*x^8+4*x^7+9*x^6+4*x^5+4*x^4+7*x^3+9*x^2+x+4)/(x^12-1) + O(x^100))

Formula

a(n) = A010888(A001254(n)).

a(n) = a(n-12).

G.f.: -(x^11 +9*x^10 +7*x^9 +4*x^8 +4*x^7 +9*x^6 +4*x^5 +4*x^4 +7*x^3 +9*x^2 +x +4) / (x^12 -1).

Extensions

Extended by Ray Chandler, Aug 27 2015