login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)
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 Fröhlich, 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 14 07:13 EST 2019. Contains 329111 sequences. (Running on oeis4.)