A211411 Largest m associated with n-th Pillai prime (A063980).

18, 18, 43, 18, 33, 63, 55, 69, 86, 101, 16, 50, 102, 165, 64, 210, 153, 225, 259, 177, 40, 247, 252, 220, 225, 122, 343, 297, 230, 303, 375, 316, 366, 74, 300, 311, 410, 463, 400, 370, 442, 188, 395, 377, 458, 426, 274, 327, 546, 334, 383, 324, 495, 498, 457, 643, 444, 553, 506, 359, 712, 502, 681, 369, 514

Offset: 1

Author

Charles R Greathouse IV, Feb 10 2013

Keywords

• nonn

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• G. E. Hardy and M. V. Subbarao, A modified problem of Pillai and some related questions, Amer. Math. Monthly 109:6 (2002), pp. 554-559.

Crossrefs

Trivially a(n) >= A063828(n). Cf. A063980.

Programs

PARI

last(p)=if(p==23,18,my(t=Mod(1/120,p));forstep(m=p-6,8,-1,t/=m; if(t==-1,return(m-1))))
Pillai(p)=my(t=Mod(5040, p)); for(m=8, p-2, t*=m; if(t==-1 && p%m!=1, return(1))); 0
apply(last, select(Pillai, primes(300)))

Formula

19 <= a(n) <= p-7 for n > 11, where p = A063980(n).