

A284904


The number of integers k less than 2^n whose decimal representation of their reciprocals has an odd periodic length.


0



0, 0, 1, 2, 5, 10, 20, 40, 80, 150, 280, 522, 965, 1802, 3393, 6426, 12197, 23236, 44419, 85116, 163543, 314837, 607440, 1174134, 2273619, 4409116, 8561931, 16646790, 32404446, 63145533, 123173667
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OFFSET

0,4


COMMENTS

The number of terms in A284601 less than 2^n.


LINKS

Table of n, a(n) for n=0..30.
Index entries for sequences related to decimal expansion of 1/n


FORMULA

log(a(n)) is approximately 0.33 + 0.727n  0.643sqrt(n).


EXAMPLE

a(5)=32 because the reciprocals of {3, 6, 9, 12, 15, 18, 24, 27, 30, 31} all have an odd period length, i.e.; {1, 1, 1, 1, 1, 1, 1, 3, 1, 15}


MATHEMATICA

f[n_] := Mod[ Length[ RealDigits[1/n][[1, 1]]], 2]; s = 0; k = 1; lst = {}; Do[ While[k < 2^n, s += f@k; k++]; AppendTo[lst, s], {n, 0, 18}] (* or *)
g[n_] := Mod[ MultiplicativeOrder[10, FixedPoint[ Quotient[#, GCD[#, 10]] &, n]], 2]; h[n_] := Length@ Most@ Flatten@ Table[2^i*5^j, {i, 0, n}, {j, 0, Log[5, 2^(n i)]}]; s = 0; k = 1; lst = {}; Do[ While[k < 2^n, s += g@k; k++]; AppendTo[lst, s  h[n]], {n, 0, 30}]


CROSSREFS

Cf. A284601.
Sequence in context: A327287 A296122 A293324 * A084215 A024810 A049938
Adjacent sequences: A284901 A284902 A284903 * A284905 A284906 A284907


KEYWORD

nonn


AUTHOR

Robert G. Wilson v, Apr 05 2017


STATUS

approved



