A007737 - OEIS

%I #28 Aug 26 2024 04:55:29

%S 1,1,1,1,1,1,2,1,1,1,10,1,12,2,1,1,16,1,9,1,2,10,11,1,5,12,1,2,14,1,6,

%T 1,10,16,2,1,4,9,12,1,40,2,3,10,1,11,23,1,14,5,16,12,26,1,10,2,9,14,

%U 58,1,60,6,2,1,12,10,33,16,11,2,35,1,36,4,5,9,10,12,78,1,1,40,82,2,16,3,14,10

%N Period of repeating digits of 1/n in base 6.

%C Not multiplicative. Smallest counterexample: a(77)=10, but a(7) = 2 and a(11) = 10. - _Mitch Harris_, May 16 2005.

%H T. D. Noe, <a href="/A007737/b007737.txt">Table of n, a(n) for n=1..1000</a>

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

%t DigitCycleLength[r_Rational, b_Integer?Positive] := MultiplicativeOrder[b, FixedPoint[ Quotient[#, GCD[#, b]] &, Denominator[r]]]; DigitCycleLength[1, b_Integer?Positive] = 1; Array[ DigitCycleLength[1/#, 6] &, 80] (* _Robert G. Wilson v_, Jun 10 2011 *)

%t a[n_] := MultiplicativeOrder[6, n/Times @@ ({2, 3}^IntegerExponent[n, {2, 3}])]; Array[a, 100] (* _Amiram Eldar_, Aug 26 2024 *)

%o (PARI) a(n)=znorder(Mod(6, n/2^valuation(n, 2)/3^valuation(n, 3))); \\ _Joerg Arndt_, Dec 14 2014

%Y Cf. A007733 (base 2), A007734 (3), A007735 (4), A007736 (5), A007738 (7), A007739 (8), A007740 (9), A007732 (10).

%K nonn,base

%O 1,7

%A _N. J. A. Sloane_, Hal Sampson (hals(AT)easynet.com)

%E More terms from _David W. Wilson_