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

1,2

Comments

The sequence is periodic with period 9.

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).

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)).

Example

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

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 *)

Prog

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

Crossrefs

Cf. A001844, A010888.

Sequence in context: A188932 A366162 A195428 * A343564 A004446 A115409

Adjacent sequences: A254370 A254371 A254372 * A254374 A254375 A254376

Keyword

nonn,easy,base

Author

Colin Barker, Jan 29 2015

Status

approved