A272633 Discriminator of the primes: Least m > 0 such that (prime(1),...,prime(n)) are all different mod m; a(0) = 0 by convention.

0, 1, 2, 4, 6, 7, 7, 13, 13, 13, 19, 19, 19, 23, 23, 23, 31, 31, 31, 33, 37, 37, 43, 43, 47, 49, 53, 53, 53, 55, 61, 63, 67, 73, 73, 75, 75, 79, 83, 83, 89, 89, 91, 91, 97, 103, 103, 109, 113, 113, 115, 117, 119, 121, 121, 121, 121, 121, 139, 139, 141, 141, 151, 153, 157, 157, 159, 167, 169, 169, 175, 181, 181, 183, 187

Offset: 0

Author

M. F. Hasler, May 04 2016

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000 (first 5001 terms from M. F. Hasler)
• Arnold, L. K.; Benkoski, S. J.; and McCabe, B. J.; The discriminator (a simple application of Bertrand's postulate). Amer. Math. Monthly 92 (1985), 275-277.

Crossrefs

Cf. A016726, A192419, A192420.

Programs

Maple

a:= proc(n) option remember; local m;
      for m from `if`(n=1, 1, a(n-1)) while
        n<>nops({seq(ithprime(i) mod m, i=1..n)})
      do od; m
    end: a(0):=0:
seq(a(n), n=0..80);  # Alois P. Heinz, May 04 2016

Mathematica

a[0]=0; a[n_]:=Block[{m=1}, While[Length@ DeleteDuplicates@ Mod[Prime@ Range@ n, m] != n, m++]; m]; a /@ Range[0, 74] (* Giovanni Resta, May 04 2016 *)

PARI

A272633(nMax)={my(S=[],a=1);vector(nMax, n, S=concat(S,prime(n)); while(#Set(S%a)