

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
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OFFSET

0,1


COMMENTS

The sequence is periodic with period 12.


LINKS

Table of n, a(n) for n=0..107.
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).


FORMULA

a(n) = A010888(A001254(n)).
a(n) = a(n12).
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^121) + O(x^100))


CROSSREFS

Cf. A000032, A001254, A216676.
Sequence in context: A325012 A092162 A073056 * A299615 A049762 A105495
Adjacent sequences: A235941 A235942 A235943 * A235945 A235946 A235947


KEYWORD

nonn,easy,base


AUTHOR

Colin Barker, Jan 17 2014


EXTENSIONS

Extended by Ray Chandler, Aug 27 2015


STATUS

approved



