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

Author

N. J. A. Sloane, Sep 23 2001

Keywords

• nonn

Examples

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

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.

Crossrefs

Cf. A063980, A211411.

Programs

Mathematica

nn=1000; fact=1+Rest[FoldList[Times,1,Range[nn]]]; t={}; Do[p=Prime[i]; m=2; While[m
T. D. Noe, Apr 22 2011 *)

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

Extensions

More terms from Vladeta Jovovic, Sep 27 2001