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

%I A272633 #21 Oct 27 2023 21:58:22
%S A272633 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,
%T A272633 49,53,53,53,55,61,63,67,73,73,75,75,79,83,83,89,89,91,91,97,103,103,
%U A272633 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
%N A272633 Discriminator of the primes: Least m > 0 such that (prime(1),...,prime(n)) are all different mod m; a(0) = 0 by convention.
%H A272633 Alois P. Heinz, <a href="/A272633/b272633.txt">Table of n, a(n) for n = 0..10000</a> (first 5001 terms from M. F. Hasler)
%H A272633 Arnold, L. K.; Benkoski, S. J.; and McCabe, B. J.; <a href="http://www.jstor.org/stable/2323651">The discriminator (a simple application of Bertrand's postulate)</a>. Amer. Math. Monthly 92 (1985), 275-277.
%p A272633 a:= proc(n) option remember; local m;
%p A272633       for m from `if`(n=1, 1, a(n-1)) while
%p A272633         n<>nops({seq(ithprime(i) mod m, i=1..n)})
%p A272633       do od; m
%p A272633     end: a(0):=0:
%p A272633 seq(a(n), n=0..80);  # _Alois P. Heinz_, May 04 2016
%t A272633 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 *)
%o A272633 (PARI) A272633(nMax)={my(S=[],a=1);vector(nMax, n, S=concat(S,prime(n)); while(#Set(S%a)<n, a++); a)}
%Y A272633 Cf. A016726, A192419, A192420.
%K A272633 nonn
%O A272633 0,3
%A A272633 _M. F. Hasler_, May 04 2016