A267017 Digital roots of the stella octangula numbers.

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

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 * A358203 A021642 A342218

Adjacent sequences: A267014 A267015 A267016 * A267018 A267019 A267020

Keyword

nonn,base,easy

Author

Peter M. Chema, Jan 08 2016

Status

approved