A216415 -id:A216415

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A084680

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

+10
12

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

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OFFSET

1,7

COMMENTS

When n is not divisible by 2 or 5, a(n) = A007732(n). A002329 contains the nonzero terms.

A number k > 0 appears in this sequence exactly A059892(k) times. - T. D. Noe, May 18 2007

LINKS

T. D. Noe, Table of n, a(n) for n=1..1000

MAPLE

A084680 := proc(n) if gcd(n, 10) <> 1 then 0 ; elif n = 1 then 1 ; else numtheory[order](10, n) ; end if; end proc: seq(A084680(n), n=2..100) ; # R. J. Mathar, Mar 10 2010

MATHEMATICA

a[n_] := If[!CoprimeQ[n, 10], 0, MultiplicativeOrder[10, n]]; Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Nov 07 2012 *)

PROG

(PARI) a(n, b=10)=if(gcd(n, b)!=1, 0, znorder(Mod(b, n)));

vector(66, n, a(n)) \\ Joerg Arndt, Nov 15 2014

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

CROSSREFS

Cf. A007732, A002329, A070682, A216415.

KEYWORD

nonn

AUTHOR

Lekraj Beedassy, Jun 30 2003

EXTENSIONS

More terms from John W. Layman, Aug 12 2003

STATUS

approved

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