A254373 Digital roots of centered square numbers (A001844).

1, 5, 4, 7, 5, 7, 4, 5, 1, 1, 5, 4, 7, 5, 7, 4, 5, 1, 1, 5, 4, 7, 5, 7, 4, 5, 1, 1, 5, 4, 7, 5, 7, 4, 5, 1, 1, 5, 4, 7, 5, 7, 4, 5, 1, 1, 5, 4, 7, 5, 7, 4, 5, 1, 1, 5, 4, 7, 5, 7, 4, 5, 1, 1, 5, 4, 7, 5, 7, 4, 5, 1, 1, 5, 4, 7, 5, 7, 4, 5, 1, 1, 5, 4, 7, 5

Offset: 1

Author

Colin Barker, Jan 29 2015

Keywords

• nonn
• easy
• base

Comments

The sequence is periodic with period 9.

Examples

			a(3) = 4 because the 3rd centered square number is 13, the digital root of which is 4.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 1).

Crossrefs

Cf. A001844, A010888.

Programs

Mathematica

FixedPoint[Plus @@ IntegerDigits[#] &, #] & /@ Table[2 n (n + 1) + 1, {n, 0, 80}] (* Michael De Vlieger, Feb 01 2015 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 1},{1, 5, 4, 7, 5, 7, 4, 5, 1},86] (* Ray Chandler, Aug 26 2015 *)

PARI

m=4; vector(200, n, (m*n*(n-1)/2)%9+1)

Formula

a(n) = A010888(A001844(n)).

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

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