A099679 Least m such that repunit R_m is a multiple of A045572(n) (i.e., odd numbers not divisible by 5).

1, 3, 6, 9, 2, 6, 16, 18, 6, 22, 27, 28, 15, 6, 3, 6, 5, 21, 46, 42, 48, 13, 18, 58, 60, 18, 33, 66, 35, 8, 6, 13, 81, 41, 84, 44, 6, 15, 96, 18, 4, 34, 53, 108, 3, 112, 18, 48, 22, 15, 42, 21, 130, 18, 8, 46, 138, 6, 42, 148, 75, 144, 78, 39, 66, 81, 166, 78, 18, 43, 174, 178

Offset: 1

Author

Lekraj Beedassy, Oct 26 2004

Keywords

• nonn
• easy

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• Patrick de Geest, Repunits and their prime factors
• T. Granlund, Factors of 10^n - 1
• M. Kamada, Factorizations of 11...11(Repunits)
• Y. Koide, Factorization of Repunit Numbers
• P. Yiu, Factorization of Repunits R_n for n<=50, Appendix Chap. 18.5 pp. 173/360 in 'Recreational Mathematics'.

Crossrefs

Cf. A002275, A045572.

Programs

Mathematica

f[n_] := Block[{k = 1}, While[ Mod[(10^k - 1)/9, n] != 0, k++ ]; k]; f /@ Select[ 2Range[ 90] - 1, Mod[ #, 5] != 0 &] (* Robert G. Wilson v, Oct 27 2004 *)

PARI

A(n)={ \\ Least m such that n | R_m
    my(f=factor(n),s=1,t);
    for(i=1,#f[,1],
        if(f[i,1]==3,
            t=3
        ,
            t=Mod(10,9*f[i,1]);
            fordiv(f[i,1]-1,d,
                if(t^d==1,t=d;break)
            )
        );
        t*=f[i,1]^(f[i,2]-1);
        s=lcm(s,t)
    );
    s
};
a(n)=A(10*(n>>2)+[-1, 1, 3, 7][n%4+1]) \\ Least m such that A045572(n) | R_m
\\ Charles R Greathouse IV, Jul 31 2011

Extensions

Corrected and extended by Robert G. Wilson v, Oct 27 2004