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

Author

Peter M. Chema, Jan 08 2016

Keywords

• nonn
• base
• easy

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).

Crossrefs

Cf. A006003, A007588, A010888.

Programs

Mathematica

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

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

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