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A194641 Digital roots of the nonzero heptagonal numbers. 0
1, 7, 9, 7, 1, 9, 4, 4, 9, 1, 7, 9, 7, 1, 9, 4, 4, 9, 1, 7, 9, 7, 1, 9, 4, 4, 9, 1, 7, 9, 7, 1, 9, 4, 4, 9, 1, 7, 9, 7, 1, 9, 4, 4, 9, 1, 7, 9, 7, 1, 9, 4, 4, 9, 1, 7, 9, 7, 1, 9, 4, 4, 9, 1, 7, 9, 7, 1, 9, 4, 4, 9, 1, 7, 9, 7, 1, 9, 4, 4, 9, 1, 7, 9, 7, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This is a periodic sequence with period 9 and cycle 1, 7, 9, 7, 1, 9, 4, 4, 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), and as the sum of the terms contained in each cycle is 51 they also satisfy the eighth order inhomogeneous recurrence 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) = 3*(1+cos(2*n*Pi/3) +cos(4*n*Pi/3)) +(n^3 +8*n^4 +7*n^5 +5*n^6 +4*n^7 +3*n^8) mod 9.

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

a(n) = A010888(A000566(n)). - Michel Marcus, Aug 10 2015

EXAMPLE

The sixth nonzero heptagonal number is A000566(6)=81. As 8+1=9, this has digital root 9 and so a(6)=9.

MATHEMATICA

DigitalRoot[n_]:=FixedPoint[Plus@@IntegerDigits[#]&, n]; Table[DigitalRoot[ n*(5*n - 3)/2], {n, 100}]

CROSSREFS

Cf. A000566, A010888.

Sequence in context: A154168 A019644 A100639 * A248674 A108743 A177271

Adjacent sequences:  A194638 A194639 A194640 * A194642 A194643 A194644

KEYWORD

nonn,easy,base

AUTHOR

Ant King, Aug 31 2011

STATUS

approved

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Last modified April 23 07:51 EDT 2019. Contains 322381 sequences. (Running on oeis4.)