A063828 Smallest m associated with n-th Pillai prime (A063980).

14, 18, 15, 8, 18, 9, 23, 13, 86, 16, 16, 50, 102, 61, 64, 210, 97, 31, 9, 93, 40, 45, 63, 220, 91, 122, 35, 85, 198, 93, 128, 316, 366, 74, 300, 151, 290, 15, 400, 282, 22, 188, 167, 191, 360, 426, 274, 271, 456, 278, 229, 324, 135, 498, 189

Offset

1,1

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)

G. E. Hardy and M. V. Subbarao, A modified problem of Pillai and some related questions, Amer. Math. Monthly 109 (2002), no. 6, 554-559.

Example

14! + 1 == 0 (mod 23), while 23 != 1 (mod 14), where 23=A063980(1) so a(1)=14.

Mathematica

nn=1000; fact=1+Rest[FoldList[Times, 1, Range[nn]]]; t={}; Do[p=Prime[i]; m=2; While[m<p && !(Mod[p, m]!=1 && Mod[fact[[m]], p]==0), m++]; If[m<p, AppendTo[t, m]], {i, 2, PrimePi[nn]}]; t (* T. D. Noe, Apr 22 2011 *)

Prog

(PARI) first(p)=my(t=Mod(5040, p)); for(m=8, p, t*=m; if(t==-1 && p%m!=1, return(m))); 0
Pillai(p)=my(t=Mod(5040, p)); for(m=8, p-2, t*=m; if(t==-1 && p%m!=1, return(1))); 0
apply(first, select(Pillai, primes(300))) \\ Charles R Greathouse IV, Feb 10 2013

Crossrefs

Cf. A063980, A211411.

Sequence in context: A165719 A154146 A113735 * A365792 A060504 A052026

Adjacent sequences: A063825 A063826 A063827 * A063829 A063830 A063831

Keyword

nonn

Author

N. J. A. Sloane, Sep 23 2001

Extensions

More terms from Vladeta Jovovic, Sep 27 2001

Status

approved