

A302141


Multiplicative order of 16 mod 2n+1.


2



1, 1, 1, 3, 3, 5, 3, 1, 2, 9, 3, 11, 5, 9, 7, 5, 5, 3, 9, 3, 5, 7, 3, 23, 21, 2, 13, 5, 9, 29, 15, 3, 3, 33, 11, 35, 9, 5, 15, 39, 27, 41, 2, 7, 11, 3, 5, 9, 12, 15, 25, 51, 3, 53, 9, 9, 7, 11, 3, 6, 55, 5, 25, 7, 7, 65, 9, 9, 17, 69, 23, 15, 7, 21, 37, 15, 6, 5, 13, 13, 33, 81, 5, 83, 39, 9, 43, 15, 29, 89, 45, 15, 9, 10, 9, 95, 24, 3, 49, 99, 33
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OFFSET

0,4


COMMENTS

Reptend length of 1/(2n+1) in hexadecimal.
a(n) <= n; it appears that equality holds if and only if n=1 or is in A163778.  Robert Israel, Apr 02 2018


LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..10000 (first 1001 terms from Jianing Song)
Eric Weisstein's World of Mathematics, Multiplicative Order


FORMULA

a(n) = A002326(n)/gcd(A002326(n),4) = A053447(n)/gcd(A053447(n),4).


EXAMPLE

The fraction 1/13 is equal to 0.13B13B... in hexadecimal, so a(6) = 3.


MAPLE

seq(numtheory:order(16, 2*n+1), n=0..100); # Robert Israel, Apr 02 2018


MATHEMATICA

Table[MultiplicativeOrder[16, 2 n + 1], {n, 0, 150}] (* Vincenzo Librandi, Apr 03 2018 *)


PROG

(PARI) a(n) = znorder(Mod(16, 2*n+1)) \\ Felix FrÃ¶hlich, Apr 02 2018
(MAGMA) [1] cat [ Modorder(16, 2*n+1): n in [1..100]]; // Vincenzo Librandi, Apr 03 2018
(GAP) List([0..100], n>OrderMod(16, 2*n+1)); # Muniru A Asiru, Feb 25 2019


CROSSREFS

Cf. A002326, A053447, A053451, A163778.
Sequence in context: A214745 A115155 A136549 * A077924 A003569 A066670
Adjacent sequences: A302138 A302139 A302140 * A302142 A302143 A302144


KEYWORD

nonn


AUTHOR

Jianing Song, Apr 02 2018


STATUS

approved



