%I #20 Jul 08 2025 09:13:51

%S 0,0,1,0,0,3,0,0,9,0,2,7,0,8,1,2,4,3,7,3,1,1,9,3,5,8,0,7,4,2,2,2,6,6,

%T 8,0,0,4,0,1,2,0,3,6,1,0,8,3,2,4,9,7,4,9,2,4,7,7,4,3,2,2,9,6,8,9,0,6,

%U 7,2,0,1,6,0,4,8,1,4,4,4,3,3,2,9,9,8,9,9,6,9,9,0,9,7,2,9,1,8,7

%N Decimal expansion of 1/997.

%C Generalization:

%C 1/7 = sum (3^i/10^(i+1)), i >= 0,

%C 1/97 = sum (3^i/100^(i+1)), i >= 0,

%C 1/997 = sum (3^i/1000^(i+1)), i >= 0, (this sequence)

%C 1/9997 = sum (3^i/10000^(i+1)), i >= 0, ... - _Daniel Forgues_, Oct 28 2011

%C Periodic with period length 166. - _Ray Chandler_, Jan 09 2025

%H <a href="/index/Rec#order_84">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1).

%t Join[{0,0},RealDigits[1/997,10,120][[1]]] (* _Harvey P. Dale_, Jul 28 2023 *)

%o (PARI) 1/997. \\ _Charles R Greathouse IV_, Apr 02 2014

%K nonn,cons,easy

%O 0,6

%A _N. J. A. Sloane_