A275615 Decimal expansion of 22/111.

1, 9, 8, 1, 9, 8, 1, 9, 8, 1, 9, 8, 1, 9, 8, 1, 9, 8, 1, 9, 8, 1, 9, 8, 1, 9, 8, 1, 9, 8, 1, 9, 8, 1, 9, 8, 1, 9, 8, 1, 9, 8, 1, 9, 8, 1, 9, 8, 1, 9, 8, 1, 9, 8, 1, 9, 8, 1, 9, 8, 1, 9, 8, 1, 9, 8, 1, 9, 8, 1, 9, 8, 1, 9, 8, 1, 9, 8, 1, 9, 8, 1, 9, 8, 1, 9, 8, 1, 9, 8, 1, 9, 8, 1, 9, 8, 1, 9, 8, 1, 9, 8

Offset: 0

Author

Peter M. Chema, Aug 03 2016

Keywords

• nonn
• cons
• easy

Comments

Period 3: repeat [1,9,8]. Also the digital root of Nexus numbers A022522.

Other variants of this period are decimal expansions of 91/111 (.819 repeating) and 109/111 (.981 repeating).

Examples

			0.198198198198198198198198198198198198198198198198198198198...
		

Crossrefs

Cf. A010888, A022522.

Programs

Mathematica

First@ RealDigits@ N[22/111, 120] (* or *)
PadRight[{}, 120, {1, 9, 8}] (* or *)
FixedPoint[Total@ IntegerDigits@ # &, #] & /@ Table[(n + 1)^6 - n^6, {n, 0, 120}] (* Michael De Vlieger, Aug 04 2016 *)

PARI

a(n) = my(x=[1, 9, 8]); x[n%3+1] \\ Felix Fröhlich, Aug 04 2016

Formula

a(n) = A010888(A022522(n)).

a(n) = 6 - 5*cos(2*n*Pi/3) + sin(2*n*Pi/3)/sqrt(3). - Wesley Ivan Hurt, Oct 04 2018