A190301 -id:A190301 - 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

A216479 a(n) is the least multiple of n which uses only the digit 1, or a(n) = -1 if no such multiple exists.

Original entry on oeis.org

1, -1, 111, -1, -1, -1, 111111, -1, 111111111, -1, 11, -1, 111111, -1, -1, -1, 1111111111111111, -1, 111111111111111111, -1, 111111, -1, 1111111111111111111111, -1, -1, -1, 111111111111111111111111111, -1, 1111111111111111111111111111, -1, 111111111111111, -1, 111111, -1, -1, -1, 111, -1, 111111, -1, 11111, -1

Offset: 1

V. Raman, Sep 07 2012

a(n) = -1 if and only if n is a multiple of 2 or 5. See comment in A216485. - Chai Wah Wu, Jun 21 2015

Chai Wah Wu, Table of n, a(n) for n = 1..1000

Cf. A084681 (number of 1's), A190301 (multiplier).

Cf. A004290, A079339, A181060, A181061.

Array[Which[GCD[#, 10] != 1, -1, Mod[#, 3] == 0, Block[{k = 1}, While[Mod[k, #] != 0, k = 10 k + 1]; k], True, (10^MultiplicativeOrder[10, #] - 1)/9] &, 42] (* Michael De Vlieger, Dec 11 2020 *)

def A216479(n):
    if n % 2 == 0 or n % 5 == 0:
        return -1
    rem = 1
    while rem % n != 0:
        rem = rem*10 + 1
    return rem
# Azanul Haque, Nov 28 2020

A215258 Smallest number h such that (2n+1)*h is a repunit (A002275), or 0 if no such h exists.

Original entry on oeis.org

1, 37, 0, 15873, 12345679, 1, 8547, 0, 65359477124183, 5847953216374269, 5291, 48309178743961352657, 0, 4115226337448559670781893, 38314176245210727969348659, 3584229390681, 3367, 0, 3, 2849, 271, 2583979328165374677, 0

Offset: 0

N. J. A. Sloane, Sep 11 2012

nonn

T. D. Noe, Table of n, a(n) for n = 0..200

A bisection of A190301.

Table[If[GCD[n, 10] > 1, 0, k = MultiplicativeOrder[10, 9*n]; (10^k - 1)/(9*n)], {n, 1, 51, 2}] (* T. D. Noe, Sep 11 2012 *)

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.

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A216479 a(n) is the least multiple of n which uses only the digit 1, or a(n) = -1 if no such multiple exists.

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A215258 Smallest number h such that (2n+1)*h is a repunit (A002275), or 0 if no such h exists.

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Author

Keywords

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Crossrefs

Programs

Mathematica