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A194731 Digital roots of the nonzero octagonal numbers. 0
1, 8, 3, 4, 2, 6, 7, 5, 9, 1, 8, 3, 4, 2, 6, 7, 5, 9, 1, 8, 3, 4, 2, 6, 7, 5, 9, 1, 8, 3, 4, 2, 6, 7, 5, 9, 1, 8, 3, 4, 2, 6, 7, 5, 9, 1, 8, 3, 4, 2, 6, 7, 5, 9, 1, 8, 3, 4, 2, 6, 7, 5, 9, 1, 8, 3, 4, 2, 6, 7, 5, 9, 1, 8, 3, 4, 2, 6, 7, 5, 9, 1, 8, 3, 4, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This is a periodic sequence with period 9 and cycle 1, 8, 3, 4, 2, 6, 7, 5, 9 - which are also the coefficients of x in the numerator of the generating function.

LINKS

Table of n, a(n) for n=1..86.

FORMULA

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

a(n) = 45 -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) = 2(cos(14*n*Pi/9) +cos(10*n*Pi/9) +cos(2*n*Pi/3) +cos(2*n*Pi/9) +cos(Pi/3)) +(n +8*n^3 +n^4 +8*n^5 +7*n^6 +8*n^7 +4*n^8) mod 9.

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

a(n) = A010888(A000567(n)). - Michel Marcus, Aug 10 2015

EXAMPLE

The sixth nonzero octagonal number is A000567(6)=96. As 9+6=15 and 1+5=6, this has digital root 6 and so a(6)=6.

MATHEMATICA

DigitalRoot[n_]:=FixedPoint[Plus@@IntegerDigits[#]&, n]; Table[DigitalRoot[n*(3*n - 2)], {n, 100}]

CROSSREFS

Cf. A000567, A010888.

Sequence in context: A117889 A021927 A145594 * A021849 A338462 A201754

Adjacent sequences:  A194728 A194729 A194730 * A194732 A194733 A194734

KEYWORD

nonn,easy,base

AUTHOR

Ant King, Sep 02 2011

STATUS

approved

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Last modified October 15 21:38 EDT 2021. Contains 348034 sequences. (Running on oeis4.)