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

1,2

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

P. 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'.

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 *)

Prog

(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

Crossrefs

Cf. A002275, A045572.

Sequence in context: A258226 A258329 A094561 * A013663 A245223 A180593

Adjacent sequences: A099676 A099677 A099678 * A099680 A099681 A099682

Keyword

nonn,easy

Author

Lekraj Beedassy, Oct 26 2004

Extensions

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

Status

approved