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A191760 Digital root of the n-th odd square. 1
1, 9, 7, 4, 9, 4, 7, 9, 1, 1, 9, 7, 4, 9, 4, 7, 9, 1, 1, 9, 7, 4, 9, 4, 7, 9, 1, 1, 9, 7, 4, 9, 4, 7, 9, 1, 1, 9, 7, 4, 9, 4, 7, 9, 1, 1, 9, 7, 4, 9, 4, 7, 9, 1, 1, 9, 7, 4, 9, 4, 7, 9, 1, 1, 9, 7, 4, 9, 4, 7, 9, 1, 1, 9, 7, 4, 9, 4, 7, 9, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This sequence is periodic with period <1,9,7,4,9,4,7,9,1> of length nine.

Related to the continued fraction of (153727+sqrt(2207057870693))/1477642 = 1+ 1/(9+1/(7+1/...)). - R. J. Mathar, Jun 27 2011

LINKS

Table of n, a(n) for n=1..81.

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

FORMULA

a(n)= 3*(1+cos(2(n-2)pi/3)+cos(4(n-2)pi/3)) +mod( (1+n)(1+7n-7n^2+7n^3+n^4-n^5+3n^6+3n^7), 9).

a(n)=a(n-9).

a(n)=51-a(n-1)-a(n-2)-a(n-3)-a(n-4)-a(n-5)-a(n-6)-a(n-7)-a(n-8).

a(n) = A010888(A016754(n)).

G.f.: x(1+9x+7x^2+4x^3+9x^4+4x^5+7x^6+9x^7+x^8)/( (1-x)*(1+x+x^2)*(1+x^3+x^6) ) (note that the coefficients of x in the numerator are precisely the terms that constitute the periodic cycle of the sequence).

a(n) = A056992(2n-1). - R. J. Mathar, Jun 27 2011

EXAMPLE

The fifth, odd square number is 81 which has digital root 9. Hence a(5)=9.

MATHEMATICA

DigitalRoot[n_Integer?Positive]:=FixedPoint[Plus@@IntegerDigits[#]&, n]; DigitalRoot[#] &/@((2#-1)^2 &/@Range[81])

LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 1}, {1, 9, 7, 4, 9, 4, 7, 9, 1}, 81] (* Ray Chandler, Aug 25 2015 *)

CROSSREFS

Cf. A010888, A016754.

Sequence in context: A155958 A010546 A232735 * A237841 A109846 A096230

Adjacent sequences:  A191757 A191758 A191759 * A191761 A191762 A191763

KEYWORD

nonn,base,easy

AUTHOR

Ant King, Jun 17 2011

STATUS

approved

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Last modified December 10 00:54 EST 2019. Contains 329885 sequences. (Running on oeis4.)