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A235944
Digital roots of squares of Lucas numbers.
0
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
0,1
COMMENTS
The sequence is periodic with period 12.
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).
EXAMPLE
a(5)=4 because A000032[5]=11 and the digital root of 11*11 = 121 is 4.
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 *)
PROG
(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))
CROSSREFS
KEYWORD
nonn,easy,base
AUTHOR
Colin Barker, Jan 17 2014
EXTENSIONS
Extended by Ray Chandler, Aug 27 2015
STATUS
approved