A007736 Period of repeating digits of 1/n in base 5.

1, 1, 2, 1, 1, 2, 6, 2, 6, 1, 5, 2, 4, 6, 2, 4, 16, 6, 9, 1, 6, 5, 22, 2, 1, 4, 18, 6, 14, 2, 3, 8, 10, 16, 6, 6, 36, 9, 4, 2, 20, 6, 42, 5, 6, 22, 46, 4, 42, 1, 16, 4, 52, 18, 5, 6, 18, 14, 29, 2, 30, 3, 6, 16, 4, 10, 22, 16, 22, 6, 5, 6, 72, 36, 2, 9, 30, 4, 39, 4, 54, 20, 82, 6, 16, 42, 14, 10, 44

Offset: 1

Author

N. J. A. Sloane, Hal Sampson (hals(AT)easynet.com), David W. Wilson

Keywords

• nonn
• base

Links

• T. D. Noe, Table of n, a(n) for n=1..1000
• Index entries for sequences related to decimal expansion of 1/n

Programs

Mathematica

f[n_] := MultiplicativeOrder[5, n/(5^IntegerExponent[n, 5])]; Array[f, 80] (* Robert G. Wilson v, Jun 10 2011 *)
Table[Length[RealDigits[1/n,5][[1,1]]],{n,90}]/.(0->1) (* Harvey P. Dale, Dec 28 2016 *)

PARI

A007736(n,bas)={ local(p) ; for(sp=2,1000000, for(s=1,sp-1, p=sp-s ; if( ((bas^p-1)*bas^s) % n == 0, return(p) ; ) ; ) ; ) ; return(-1) ; } { for(n=1,100, print(n," ",A007736(n,5)) ; ) ; } \\ R. J. Mathar, Aug 30 2006

PARI

a(n)=znorder(Mod(5,n/5^valuation(n,5))) \\ Charles R Greathouse IV, Jun 10 2011