A121341 Number of decimal places before 1/n either recurs or terminates.

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, 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, 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

Offset

1,4

Comments

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.

Links

T. D. Noe, Table of n, a(n) for n = 1..1000 (corrected by Sean A. Irvine, Apr 29 2022)

Index entries for sequences related to decimal expansion of 1/n

Formula

a(n) = A051628(n) + A051626(n). - Sean A. Irvine, Apr 13 2022

Example

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

Mathematica

a[n_] := Max[IntegerExponent[n, 2], IntegerExponent[n, 5]] + Length[RealDigits[1/n][[1, -1]]];
Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Jul 20 2022 *)

Crossrefs

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

Cf. A051626, A051628.

Sequence in context: A060550 A099206 A269223 * A241737 A174959 A126093

Adjacent sequences: A121338 A121339 A121340 * A121342 A121343 A121344

Keyword

base,easy,nice,nonn

Author

Anthony C Robin, Aug 29 2006

Extensions

More terms from T. D. Noe, Aug 30 2006

Additional comments from R. J. Mathar, Aug 30 2006

Status

approved