A338753 Number of integers less than n with the same period of reciprocal as n.

0, 1, 0, 2, 3, 1, 0, 4, 2, 5, 0, 3, 1, 2, 4, 6, 0, 5, 0, 7, 3, 1, 0, 6, 8, 4, 0, 5, 0, 7, 0, 9, 2, 1, 6, 8, 1, 1, 7, 10, 0, 8, 0, 3, 9, 1, 0, 10, 0, 11, 2, 9, 0, 2, 4, 10, 2, 1, 0, 11, 0, 1, 11, 12, 12, 5, 0, 3, 2, 13, 0, 12, 0, 3, 13, 3, 14, 15, 1, 13, 0, 1, 0, 16, 4, 1, 2, 6, 0, 14

Offset

1,4

Links

Table of n, a(n) for n=1..90.

Eric Weisstein's World of Mathematics, Repeating Decimal

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

Formula

a(n) = |{j < n : A051626(j) = A051626(n)}|.

Example

a(14) = 2 because A051626(14) = 6 and also A051626(7) = A051626(13) = 6.
More specifically,
1/7  = 0.142857(142857)...  (period 6),
1/13 = 0.076923(076923)...  (period 6),
1/14 = 0.0714285(714285)... (period 6).

Mathematica

Table[Length[Select[Range[n - 1], Length[RealDigits[1/#][[1, -1]]] == Length[RealDigits[1/n][[1, -1]]] &]], {n, 90}]

Crossrefs

Cf. A051626.

Sequence in context: A352067 A368486 A178245 * A167666 A115352 A275808

Adjacent sequences: A338750 A338751 A338752 * A338754 A338755 A338756

Keyword

nonn,base

Author

Ilya Gutkovskiy, Nov 06 2020

Status

approved