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A267017 Digital roots of the stella octangula numbers. 3
0, 1, 5, 6, 7, 2, 3, 4, 8, 9, 1, 5, 6, 7, 2, 3, 4, 8, 9, 1, 5, 6, 7, 2, 3, 4, 8, 9, 1, 5, 6, 7, 2, 3, 4, 8, 9, 1, 5, 6, 7, 2, 3, 4, 8, 9, 1, 5, 6, 7, 2, 3, 4, 8, 9, 1, 5, 6, 7, 2, 3, 4, 8, 9, 1, 5, 6, 7, 2, 3, 4, 8, 9, 1, 5, 6, 7, 2, 3, 4, 8, 9, 1, 5, 6, 7, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

This is the digital root sequence for A007588 and for A006003, two nice sequences relating to structured numbers (hexagonal anti-diamond numbers (vertex structure 13) and trigonal diamond numbers (vertex structure 4) respectively).

It is composed of all 9 of the nonzero digits, period 9. Root digits increase by 1 in sets of 3 [i.e., "5, 6, 7", "2, 3, 4" and "8, 9, 1"]. - Peter M. Chema, Aug 21 2016

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

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

FORMULA

a(n) = A010888(A007588(n)).

From Colin Barker, Jan 10 2016: (Start)

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

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

(End)

a(n) = A010888(A006003(n)). - Peter M. Chema, Aug 17 2016

MATHEMATICA

FixedPoint[Total@ IntegerDigits@ # &, #] & /@ Table[n (2 n^2 - 1), {n, 0, 108}] (* Michael De Vlieger, Jan 09 2016 *)

PROG

(PARI) A010888(n)=if(n, (n-1)%9+1);

a(n) = A010888(n*(2*n^2 - 1)); \\ Michel Marcus, Jan 10 2016

(PARI) concat(0, Vec(x*(1+5*x+6*x^2+7*x^3+2*x^4+3*x^5+4*x^6+8*x^7+9*x^8) / ((1-x)*(1+x+x^2)*(1+x^3+x^6)) + O(x^100))) \\ Colin Barker, Jan 10 2016

CROSSREFS

Cf. A006003, A007588, A010888.

Sequence in context: A030178 A038458 A284361 * A021642 A299082 A171423

Adjacent sequences:  A267014 A267015 A267016 * A267018 A267019 A267020

KEYWORD

nonn,base,easy

AUTHOR

Peter M. Chema, Jan 08 2016

STATUS

approved

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Last modified October 17 00:03 EDT 2019. Contains 328103 sequences. (Running on oeis4.)