A121341 - OEIS

%I #25 Jul 20 2022 15:20:58

%S 0,1,1,2,1,2,6,3,1,1,2,3,6,7,2,4,16,2,18,2,6,3,22,4,2,7,3,8,28,2,15,5,

%T 2,17,7,3,3,19,6,3,5,7,21,4,2,23,46,5,42,2,16,8,13,4,3,9,18,29,58,3,

%U 60,16,6,6,7,3,33,18,22,7,35,4,8,4,3,20,6,7,13,4,9,6,41,8,17,22,28,5,44,2,6

%N Number of decimal places before 1/n either recurs or terminates.

%C In this sequence, the repeating decimals (e.g., 1/7) are treated differently from nonrepeating decimals (e.g., 1/5). If they are treated the same, then a(2)=2, a(4)=3, a(5)=2, a(8)=4, a(10)=2, ... and we obtain A054710. The two sequence differ only for n = 2^j * 5^k.

%H T. D. Noe, <a href="/A121341/b121341.txt">Table of n, a(n) for n = 1..1000</a> (corrected by Sean A. Irvine, Apr 29 2022)

%H <a href="/index/1#1overn">Index entries for sequences related to decimal expansion of 1/n</a>

%F a(n) = A051628(n) + A051626(n). - _Sean A. Irvine_, Apr 13 2022

%e 1/592 = 0.0016891891891... starts with 4 decimals (0016, zeros counted) and has period 3 (digits 891) to yield a(592) = 4 + 3 = 7.

%t a[n_] := Max[IntegerExponent[n, 2], IntegerExponent[n, 5]] + Length[RealDigits[1/n][[1, -1]]];

%t Table[a[n], {n, 1, 100}] (* _Jean-François Alcover_, Jul 20 2022 *)

%Y A007732 is the length of the periods and serves as a lower bound. Cf. A061075.

%Y Cf. A051626, A051628.

%K base,easy,nice,nonn

%O 1,4

%A _Anthony C Robin_, Aug 29 2006

%E More terms from _T. D. Noe_, Aug 30 2006

%E Additional comments from _R. J. Mathar_, Aug 30 2006