A275704 Digital root of n + (n+1)^2.

1, 5, 2, 1, 2, 5, 1, 8, 8, 1, 5, 2, 1, 2, 5, 1, 8, 8, 1, 5, 2, 1, 2, 5, 1, 8, 8, 1, 5, 2, 1, 2, 5, 1, 8, 8, 1, 5, 2, 1, 2, 5, 1, 8, 8, 1, 5, 2, 1, 2, 5, 1, 8, 8, 1, 5, 2, 1, 2, 5, 1, 8, 8, 1, 5, 2, 1, 2, 5, 1, 8, 8, 1, 5, 2, 1, 2, 5, 1, 8, 8, 1, 5, 2, 1, 2, 5, 1, 8, 8, 1, 5, 2, 1, 2, 5, 1, 8, 8, 1, 5, 2, 1, 2, 5, 1, 8, 8, 1, 5, 2, 1, 2, 5, 1, 8, 8, 1, 5, 2, 1

Offset: 0

Author

Peter M. Chema, Aug 05 2016

Keywords

• nonn
• easy
• base

Comments

Period 9: repeat [1,5,2,1,2,5,1,8,8].

When expressed starting from the 9th term, i.e., 8,1,5,2,1,2,5,1,8,8,1,5,2,1,2,5,1,8, etc., the sequence is palindromic.

Decimal expansion is 50708396/333333333.

Links

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

Crossrefs

Cf. A010888, A028387.

Programs

Mathematica

Table[FixedPoint[Total@ IntegerDigits@ # &, n + (n + 1)^2], {n, 0, 120}] (* or *)
PadRight[{}, 120, {1, 5, 2, 1, 2, 5, 1, 8, 8}] (* Michael De Vlieger, Aug 07 2016 *)

Formula

a(n) = A010888(A028387(n)).

G.f.: ( -1 - 5*x - 2*x^2 - x^3 - 2*x^4 - 5*x^5 - x^6 - 8*x^7 - 8*x^8 ) / ( (x-1)*(1+x+x^2)*(x^6+x^3+1) ). - R. J. Mathar, Jan 07 2019