A099794 - OEIS

%I #11 Sep 08 2022 08:45:15

%S 1,1,5,43,2291,6397,423953,2579419,30364247,77544004469,1277242663471,

%T 70250377083373,3909462041753561,101888460343995907,

%U 8217087542785091183,2455846588270412484317,38974424104246263663539

%N a(n) = smallest integer k such that k*prime(n) == 1 mod j for each integer j with 1<j<prime(n).

%F a(n) = A094998(n) / prime(n).

%t a[1] = a[2] = 1; a[n_] := Module[{p, m, r, r0, r1}, p = Prime[n]; m = LCM @@ Range[2, p-1]; r = Reduce[k>0 && p*k + m*j == 1, {k, j}, Integers]; r0 = r /. C[_] -> 0; r1 = r /. C[_] -> 1 ; If[r0 === False, r1[[1, 2]], Min[r0[[1, 2]], r1[[1, 2]]]]]; Table[a[n], {n, 1, 20}] (* _Jean-François Alcover_, Feb 09 2015 *)

%o (Magma) /* By definition (slow): */

%o S:=[]; for n in [1..9] do k:=1; while not forall{j: j in [2..NthPrime(n)-1] | IsOne(k*NthPrime(n) mod j)} do k:=k+1; end while; Append(~S, k); end for; S; /* or */

%o [p eq 2 select 1 else Modinv(p, Lcm([1..p-1])): p in PrimesUpTo(60)];// _Bruno Berselli_, Feb 08 2015

%Y Cf. A094998, A099795, A099796.

%K nonn

%O 1,3

%A _Ray Chandler_, Oct 29 2004