A211411 - OEIS

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

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OFFSET

1,1

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.

FORMULA

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

PROG

(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)))