A216479 -id:A216479 - cp's OEIS frontend

A084681 Order of 10 modulo 9n [i.e., least m such that 10^m = 1 (mod 9n)] or 0 when no such number exists.

1, 0, 3, 0, 0, 0, 6, 0, 9, 0, 2, 0, 6, 0, 0, 0, 16, 0, 18, 0, 6, 0, 22, 0, 0, 0, 27, 0, 28, 0, 15, 0, 6, 0, 0, 0, 3, 0, 6, 0, 5, 0, 21, 0, 0, 0, 46, 0, 42, 0, 48, 0, 13, 0, 0, 0, 18, 0, 58, 0, 60, 0, 18, 0, 0, 0, 33, 0, 66, 0, 35, 0, 8, 0, 0, 0, 6, 0, 13, 0, 81, 0, 41, 0, 0, 0, 84, 0, 44, 0, 6, 0, 15, 0

Offset: 1

Lekraj Beedassy, Jun 30 2003

nonn

Robert Israel, Table of n, a(n) for n = 1..10000
K. Matthews, Finding the order of a (mod m)

Cf. A084680, A190301, A216479.

List([1..100],n->OrderMod(10,9*n)); # Muniru A Asiru, Feb 26 2019

f:= proc(n)
if igcd(n,10)>1 then 0 else numtheory:-order(10,9*n) fi
end proc:
map(f, [$1..100]); # Robert Israel, Feb 22 2019

a[n_] := If[GCD[10, 9n] != 1, 0, MultiplicativeOrder[10, 9n]];
Array[a, 100] (* Jean-François Alcover, Jul 19 2020 *)

a(n) = if (gcd(10, 9*n) != 1, 0, znorder(Mod(10, 9*n))); \\ Michel Marcus, Feb 23 2019

From Robert Israel, Feb 22 2019: (Start)
a(n) = A084680(9*n).
If n is not divisible by 3, a(n) = A084680(n).
Otherwise a(n) can be either A084680(n), 3*A084680(n) or 9*A084680(n). (End)

More terms from John W. Layman, Oct 09 2003

A190301 Smallest number h such that n*h is a repunit (A002275), or 0 if no such h exists.

Original entry on oeis.org

1, 0, 37, 0, 0, 0, 15873, 0, 12345679, 0, 1, 0, 8547, 0, 0, 0, 65359477124183, 0, 5847953216374269, 0, 5291, 0, 48309178743961352657, 0, 0, 0, 4115226337448559670781893, 0, 38314176245210727969348659, 0, 3584229390681, 0, 3367, 0, 0, 0, 3, 0, 2849, 0, 271, 0

Offset: 1

Jaroslav Krizek, May 07 2011

nonn

			For n = 7: a(7) = 15873 because 7 * 15873 = 111111. Repunit 111111 is the smallest repunit with prime factor 7.

Robert G. Wilson v, Table of n, a(n) for n = 1..1001 (first 300 terms from T. D. Noe)

Cf. A084681 (repunit length), A216479 (the repunit).
Cf. A050782 = the smallest number h such that n*h is palindromic number, A083117 = the smallest number h such that n*h is repdigit number.
Cf. A004290, A079339, A181060, A181061.

Table[If[GCD[n, 10] > 1, 0, k = MultiplicativeOrder[10, 9*n]; (10^k - 1)/(9*n)], {n, 100}] (* T. D. Noe, May 08 2011 *)

a(n)=if(gcd(n,10)>1, 0, (10^znorder(Mod(10,9*n))-1)/9/n) \\ Charles R Greathouse IV, Aug 28 2016

cp's OEIS Frontend

A084681 Order of 10 modulo 9n [i.e., least m such that 10^m = 1 (mod 9n)] or 0 when no such number exists.

Views

Author

Keywords

Links

Crossrefs

Programs

GAP

Maple

Mathematica

PARI

Formula

Extensions