A099794 a(n) = smallest integer k such that k*prime(n) == 1 mod j for each integer j with 1

1, 1, 5, 43, 2291, 6397, 423953, 2579419, 30364247, 77544004469, 1277242663471, 70250377083373, 3909462041753561, 101888460343995907, 8217087542785091183, 2455846588270412484317, 38974424104246263663539

Offset: 1

Author

Ray Chandler, Oct 29 2004

Keywords

• nonn

Crossrefs

Cf. A094998, A099795, A099796.

Programs

Magma

/* By definition (slow): */
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 */
[p eq 2 select 1 else Modinv(p, Lcm([1..p-1])): p in PrimesUpTo(60)];// Bruno Berselli, Feb 08 2015

Mathematica

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 *)

Formula

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